Looks very much like foliage of woodland anemone (Anemone japonica hybrids or A. robustissima). That one spreads somewhat and should develop flower stalks somewhen, pink or white

Thanks Jeb I thought it might be :)

An Aloe of some sort ... one that could use significantly more light, too.

The leaves appear to have tubercules on their surfaces, not something Aloe vera has. Aloe vera has marginal teeth but not surface tubercules. Could be a different Aloe. Does need more light, though. Put by window, not on counter.