Is there a way to fix the lathe - given that I have a nicely outfitted
shop with old tools that probably won't hold to the tolerances I
suspect I will need to true up the lathe?

There's two ways. One is scraping everything back in. Slow and tedious work.
if you're interested the bible on the subject is "Machine tool
Reconditioning" by Connelly.

Other route for a smaller machine like yours is to take it clear apart and
send it out to a shop to have it reground.

Your choice, have you got more time or money? (I don't have either- my
machines just get used as is)

Karl