Everything works with a little trick. In order to have console working you have to run application from the terminal (which is later to become your console).
$ env WINEPREFIX="/home/mwalczak/.wine" wine C:\\Program\ Files\ \(x86\)\\Corona\ Labs\\Corona\ SDK\\Corona\ Simulator.exe
To build apps for android you'll also need to install jdkx86 on your wine.
What does not
What was not tested
Premium Corona SDK, building for platforms other than android
|Operating system||Test date||Wine version||Installs?||Runs?||Used|
|Current||Ubuntu 13.10 "Saucy" amd64 (+ variants like Kubuntu)||Mar 09 2014||1.4.1||Yes||Yes||Platinum||an anonymous user|