There are two issues. The first is that the game complains that it can not load global data. To get around this, one has to:

1) copy contents of DAO directory (located under wherever Liberation Day was installed) to $WINEPREFIX/drive_d/windows/system32
2) set dll override for each copied *.dll
3) launch command line under Wine and register
regsvr32 /s c:\windows\system32\DAO350.DLL
regsvr32 /s c:\windows\system32\MSJET35.DLL
4) install vb6run and jet40 with winetricks

The second issue (and that seems to be shared with original Fallen Haven) is that though the game now launches, sprites are not rendered correctly. Results are partially random and may range from black screen to only ground plane visible to most of the stuff (units, structures, trees etc.) visible, but not all. This may be related to 256 colour mode the game uses, but my experiments with Xephyr to force 8bit colour depth were unsuccessful (black screen).

So I am leaving this bit of knowledge here for sake of science and for future generations. Perhaps one day somebody will crack the second issue too.