It sounds like either the muscles used for eating get so fatigued (since you have tmj and probably don't chew as a "normal" person would) that your tongue and lower lip just can't keep going, or you are pinching a nerve when chewing. Do your cheeks gets tired also when eating? I ask that because it sure would be better if it's just the muscles getting too tired. If you think that it is that problem, you might want to either go to a good, knowledgeable physical therapist to learn some exercises for that part of the face and neck, or you could just do some exercises on your own. There are a few good books and websites that show some excellent tmj exercises (nismat.Org/ptcor/tmj/ is one). The pinched nerve theory would be more difficult to diagnose, locate and fix. A doctor would definitely have to be involved.
I don't think a liquid or soft diet for a few weeks would be the answer even though doctors tell us to do that because it sounds like you need to build up strength, not rest, but this is also another "treatment" option as you probably know.
As a long time tmj sufferer, are you under the care of a tmj dentist? Do you wear a bite splint or anything similar? I'm just curious as after 25 years of this stupid tmj, I do have a tmj "specialist" but it's amazing how few "specialists" know very much about tmj, especially if you develop anything different than the usual symptoms.
I hope you are able to get everything back working as it should soon. I'd be curious to know what you find out if you don't mind writing back (either here or a private message). Good "luck" (even though I don't believe in luck, i've never been able to come up with a better sentiment for what I want to say.) oh well. :)
god bless...
Carol