I just recently started LWOTC and I can run mods fine. First of all, based on what you are saying, the game will show as "Not Responding" for a minute or two while the launcher is loading up all the mods into the game. I recommend just being patient, but if it continues, definitely make sure you have unsubscribed from X2WOTCCommunityHIghlander and are only using the [BETA] version that comes with LWOTC.

Also, make sure you follow every step in the install process as it does require you to delete some files from a different, XCOM 2 related, directory before loading up the game (and without any mods other than the ones necessary for LWOTC) for the first time. Once you load it and it re-creates those files, you can then close the game and start adding mods freely.

So far I have had only two mods that wouldn't work properly or had a discrepancy warning when loading LWOTC, but everything else (cosmetic only) has worked fine.

I have found a solution. After following all the steps exactly, still not working. waiting even 5 minutes, but XCOM app not responding. So i "accidentaly" subscribe again the mod, that has to be not subscribed ( i assume step 1 in guide) and HURAY the game runs. So far, 10 missions, no problems founds.
Playing only with the modes mentioned in the guide. no other added into the Alternative launcher

I've been running lwotc for about 20 hours and now suddenly it won't load saves. It just sits there for minutes loading interminably.