I'm sorry that Lemmix doesn't work on WINE, but Dullstar, consider that minimac94 may have perfectly valid reason to not want to use Customize Lemmings. For example, consider the replay and fast forward features in Lemmix.
Anyway, I would answer minimac94's question, except I don't know enough about what's not working for him right now. Can you at least open your levelpaks in Lemmix? You should at least be able to do that. When you go to "Open..." in the "File" menu, at the window that pops up, Under "Files of Type", select "DOS Levelpack file (*.dat)". The window will now list .dat files, browse to your levelpak file and select it for opening.
An "Edit DOS Levelpack" window should now pop up, listing all the levels in that levelpack. Right-click on the window and select "Change Viewer Style..." in the popup menu. A "Select Style" window will pop up, select "Custom Lemmings" and click OK.
You can go to individual levels by clicking on the level in the "Edit DOS Levelpack" window, and play them by pressing F2. Hope this helps.