I may just go ahead and put a boatload of lavender there. I really like
that stuff and it seems to thrive in the sun.

If lavender (or other choices like thyme, creeping thyme, etc) will
grow, then you probably have many choices. I was assuming the spot
was too shady and the soil too poor for that (and the "does not harbor
vermin" criterion I was also having trouble with, as I would think
that "vermin" - or "wildlife" according to one's perspective - would
be happy with a fairly wide variety of vegetation, potentially).

If Pachysandra doesn't excite you, it is unlikely to be your only
choice, especially if you do end up doing at least a bit of soil
improvement.

I'd consider one plant for the sunny half and something different for
the shady half. Especially if whatever you try first only thrives on
one side or the other.