I figured it out! I noticed there were some extra files in .wine/drive_c/windows/system32/spool/drivers/color/, some of which I guessed were from my experimenting, but I wasn't sure, so on a whim I tried removing them all and restarting Lightroom, and then I saw a file being created called 26d6cc1d628462ebbe35d4d50d34c8bfa086b9c7.icm. So I closed Lightroom, and overwrote that strangely-named file with my colorhug.icc, and it worked, the colours now look the same in GIMP, geeqie and Lightroom :-)

So the solution is: delete all the files in that folder, and see what file is created by Lightroom on startup, then overwrite that.

EDIT: Actually, if you use it with a new monitor, don't delete all the files in that folder, let the sRGB Color Space Profile.icm stay. That file is used when LR can't scrape a profile from the monitor itself (some monitors come with built-in profiles), so if you try a new monitor, you'd better have that sRGB file there, or LR may show the pictures as big gray blobs and such (until you turn on soft-proofing, where it'll use a different profile).