If Bethesda Introduces the Lilmothiit to the Games, In what way do you think they will go about doing it?

Well, it would depend. I doubt they will be added as a playable race, since they are really similiar to khajiit and would look like a copy of them. However, if they could be encountered in-game, maybe it would be an opportunity to trade with their tribes? They lived in primitive societies and were possibly nomadic, so it could be used to trade with them and maybe even hire some of them. Since we don't have much lore on them and they are most likely extinct, this is all a big speculation, but very interesting nonetheless! 

They'd probably have a role similar to snow-elves, as they're believed to be extinct. It would be cool to see a secret colony.

Because they're vulpine, they would have much the same stats and stuff as Khajiit, so I think that Daraya is correct in saying there is little chance they'd be playable. But, they would have vulpine traits such as strength and heightened smell, so they may fill the long-anticipated role of...

Dog-jiit.

Elder Scrolls already has plenty of furry-bait. Allowing the Lilmothiit to be anything more than a footnote in the history of Tamriel would probably bring about a few too many accusations of pandering to the furry demographic. Two beast races is plenty.

Then again, if the series ever travels to Akavir, we may meet many, many more beast races, and if that happens, all bets are off.

Tbh, I don't really want TES to turn into a massive fur-fest. Khajiit & Arg-onions are enough for me.

I'm a longtime member of the furry fandom and even I think that the series would be ruined by the addition of too many anthropomorphic races. They're not meant to be a focus of the games. That's probably why we still haven't had a game actually take place in Elsweyr.