Hmm... I have a Series 2 Space Black and FB Messenger has NEVER worked properly, even after deleting the app from the watch and phone several times. I would expect it to not on LTE with the latest watches as well.
On my watch, I can get messenger notifications, if I tap on it, it switches to a screen with several friends and it will slowly sync, minutes to forever. Messenger worked properly with my original Gen. 1 watch a couple years back, until Failbook found it important to update their app every few days and they broke the watch portion of it. The watch app for it certainly kills battery and it is still worthless.
Does this work for anyone?