What works
//DISCLAIMER: I didn't actually run Livezilla with a server, I just got the client program up and running, which is an achievement because normally it complains about missing fonts. The client window comes up and the Livezilla tray notification area icon goes into the right-hand end of the panel (Linux's version of the Start Bar). When you right-click on the Livezilla tray notification area icon, a menu comes up. From there you can exit (close) the Livezilla process. Clicking "open" from this menu opens the client window. Clicking on this tray notification area icon brings up the client window. Clicking on this icon after right-clicking it closes the pop-up menu, whereas "clicking away" doesn't. Loads quick, no part seems to lag from my very limited "test". System > Options brings up the options. Tabs and up and down number buttons therein work. Other fields in there work. Right and left buttons for tabs for the "Client Configuration" window work. View options work. FAQ/ Help under "Help" in the upper-left brings up the operating system's naive default web browser. The "About Livezilla" works. Link to the Livezilla website therein works, and clicking "Terms of Service" brings that up. Close button works. "Edit Servers" button and dialogue seems functional.

What does not
View > Pages > "Livezilla Startpage" is grayed-out, though maybe it is supposed to be like that because I'm not logged in or anything. Does not un-gray with Windows Enabler when Windows Enabler is ran from the same prefix.

What was not tested
The actual purpose of the program. Go ahead and laugh, but this test-data entry is here in celebration of getting past the missing font errors.

Additional Comments

Admin note: rating changed due to extremely limited testing. Reporter is unable to confirm that actual use works, and several bugs have been filed for this app.

I am rating this as "gold" because from what I have tested so far, even though the test doesn't include its "actual" use, what I have tested of it works flawlessly after some tweaking, which is the definition of "gold", see the rating definitions: http://appdb.winehq.org//help/?sTopic=maintainer_ratings .

Here's the mothering thread that gave rise to this AppDB entry: http://forum.winehq.org/viewtopic.php?t=12202&postdays=0&postorder=asc&start=0&sid=14890fc6c441ed96183ae25a8a28bb80

Here's how you get it to work in Wine:

The magic is composed of two parts:
1. Getting the TTF files into %windir%\Fonts - that'd be [WINEPREFIX]/drive_c/windows/Fonts
 
2. For each TTF file in the WINEPREFIX's font folder, have a corresponding registry key in HKLM\Software\Microsoft\Windows NT\CurrentVersion\Fonts - that is, in_Wine'S_registry. To be even more specific, in the Wine registry of the prefix that Livezilla is installed in.
 
Note: in the below tutorial, there are several times wine is ran from terminal. I simply typed in "wine" with other parameters. If you are running a wine executable in a location other than /usr/bin (or wherever your operating system's default location is to keep the wine executable) or have renamed the wine executable, you may need to substitute the full path or new name to your wine executable wherever I have "wine" to run the wine executable.
 
Here's what I did. I don't know if all the winetricks are nessisary, but I used them:
 
1. Installed Wine 1.3.21 (there's instructions for that eslewhere). *future-proofing* - try most recent Wine first. You don't need to go back to 1.1.39 like I did at first (but hey, I know how to complie Wine from source now).
 
2. Downloaded the normal Livezilla client installer (as opposed to the portable one - not saying the portable one won't work - just saying I haven't successfully tried it yet).
 
3. Went to my home folder (/home/shjake in my case) and made a folder named "livezilla". This can be done in Nautilus by right-clicking, clicking "Create Folder" and naming it OR you can do "mkdir $HOME/livezilla" from terminal since you're going there anyway. Well, at least that terminal command works in Linux and Mac, I don't know about the others.
 
4.  In terminal I did: "WINEPREFIX=$HOME/livezilla sh /usr/bin/winetricks gdiplus ie6 dotnet20". You may have a different path to the winetricks script; replace as necessary. In the "original" posts I found of people getting Livezilla to work in Wine, they also had winetricks install 
mdac25 and mdac28. But when I told winetricks to get mdac25 and mdac 28, it couldn't get ahold of them.
 
5. So I searched for and downloaded the mdac 2.8 installer, which I imagine makes the mdac 2.5 installer unneeded. I couldn't find the mdac 2.5 installer, but like I said, that shouldn't matter since I got the mdac 2.8 installer. In terminal, I then ran "WINEPREFIX=$HOME/livezilla wine [path to mdac 2.8 installer]". 
 
6. In terminal did: "WINEPREFIX=$HOME/livezilla wine [path to Livezilla instaler]". Went through installer.
 
7. In terminal did "WINEPREFIX=$HOME/livezilla sh /usr/bin/winetricks corefonts wininet"
 
8. Dealt with fonts. Read on.
 
Ok, more details. Whatever font(s) Livezilla complains about being missing, copy that/those font file(s) out of your Windows side and into the [WINEPREFIX]/drive_c/windows/Fonts folder (same prefix folder that you installed Livezilla into). The font files have a "TTF" file extension (last charaters of the file name which follow a dot). The font file(s) will be found on the Windows side at %windir%\Fonts - you can actually type that in the Explorer Address bar, if you are in Windows (not Internet Explorer; Explorer, a.k.a the file browser or "My Computer" or "Computer" - brought up by the Windows key (on keyboard, a.k.a "super") held down with the "e" key) ). %windir% is wherever you installed Windows to, which is probably in a folder named "WINDOWS" immediately (in the root directory of) the partition containing Windows.
If you are trying to copy the font file from within Windows to somewhere Linux or Mac OS or what-have-you can see the file (I know about NTFSprogs and 3G FUSE, but sometimes you have a virtual machine situation), Explorer recognises the font folder (or the font files - something like that) as "special" and shows the name of each font rather than the name of each file and "copy" is not present in the right-click menu. So if you can't copy the file over from your other operating system (or rather wouldn't), I recommend right-clicking on the font file, going to properties, getting the actual name of the file, opening command prompt and entering this "xcopy [path to font file, use actual file name NOT the name of the font as Explorer shows] [path to where you want it to go]". Remember that in Windows and most DOS command shells, paths are written with backslashes (\) rather than forward-slashes (/).
Ok, so get whatever fonts Livezilla is complaining about being missing into the %windir%\Fonts folder of the Wine prefix folder that you installed Livezilla to by copying in those TTF files. Get them in [WINEPREFIX]/drive_c/windows/Fonts. If you are browsing the font files from Windows, it's easy to find the font file that contains the font you are looking for because it displays the font name, rather than the file name, under the icon for each font file. If you are browsing your font files with Nautilus, it displays the actual file name, which you may or may not be able to readily correlate to the name of the font it contains. In Linux, you can open a font file with the font viewer, and it will tell you the name of the font.
But I can tell you that Microsoft Sans Serif (True Type) is MICROSS.TTF and Verdana (True Type) is simply verdana.TTF.
 
Now go to terminal and do a "WINEPREFIX=$HOME/livezilla wine regedit". Navigate to HKEY_LOCAL_MACHINE\Software\Microsoft\Windows NT\CurrentVersion\Fonts. And just so you know, HKEY_LOCAL_MACHINE is often abbreviated as "HKLM". 
For each font that Livezilla complains about, or better yet, for each font file you haven in [wineprefix]/drive_c/windows/Fonts, make sure there is a corresponding registry string value in the registry path mentioned above. If you are in the Wine registry editor, and have the contents of the Fonts key in the right pane, and you see that there is a lack of a registry value such that one of your font files in your Wine prefix is not represented, click edit in the upper-left of the registry editor, go down to "new", and then click "String Value". Name the string value the exact name of the font contained in the unrepresented font file, not the name of the font file. Don't add extra spaces to the end of the name or anything. The name must be a character-for-character match. You can find out the name of the font by opening the corresponding font file in a font viewer. Now right-click this new value you made, go to "Modify" and make the Value data be the name of the font file. Not the path to it, just its name. It knows already to look in the Fonts folder.
Keep doing that until all the font files (or at least the ones Livezilla is concerned about) are both present in the Wine prefix's font folder AND are represented in that Wine prefix's registry.
 
The missing step #9: Cagaud (at http://www.livezilla.net/forum/viewtopic.php?f=4&t=438&sid=c701c83e1a44d50b2a8e1e66069d55c5&start=20) says you should "adjust the Client Pll Frequency (value 15 is a good one) and the Visitor Pll Frequency (ideal value is 60 seconds) because otherwise the defaults values will create freq. disconnections"  I couldn't figure out how to do that. If you know how, it might make Livezilla run more stably in Wine if you do what Cagaud says.
 
The Launcher placed on your desktop to run Livezilla with wine will automatically specify the Wine prefix, so you don't have to launch Livezilla out of terminal every time if you put it in it's own prefix. At least in Linux it does that.
 
When you run Livezilla in Wine, you even get the Livezilla icon in Linux's version of the "tray notification area" - at least in Linux it does; I haven't tested that in Mac OS. You can right-click on it and bring up that little menu.
 
Once you have Livezilla and all the winetricks and font stuff to go with it installed into a Wine prefix (the livezilla folder in the example) and it's working, you can copy that folder onto an external hard drive or something, maybe put it inside an archive, and you could then quickly deploy it onto other Linux/ Mac OS/ other OS machines. Or put it on a network drive if you want to be really fast.