Hey @BrockBoyts
I'm using lr-fba-next with romset 0.173 (fba 0.2.97.38) in RetroPie 4.0.3 on a Raspberry Pi 3 and TMNT: Turtles In Time seams to run fine for me. I have both tmnt2.zip and tmnt2po.zip and they both work great.
I also have an unknown romset (I downloaded when I didn't realized you had to have romsets for different versions of MAME when I first installed RetroPie) that I'm using with lr-mame2003 and have 3 versions of TMNT: Turtles In Time and they all work fine as well.
Do you have a tmnt2.zip.cfg file in your ~/RetroPie/roms/mame-libretro/ directory by chance?
(or whatever your ROM file is with .cfg after it?)
If you haven't already, you might also try updating the RetroPie-Setup script and then update lr-mame2003 to the newest binary.