Team Sonic Racing
Yes it will. I play it on a regular switch, but I've only played it in handheld mode. To this day I still haven't played this game while my switch is docked to the tv. So it's perfectly safe to say it will absolutely work on a switch lite.
Because... SEGA MAGIC
For Mario Kart 8 Deluxe, yes you do need some steering wheels for your Joy-Cons, but not for Team Sonic Racing though. It doesn't really require motion controls.
Yes, for online races that is.