In this case "legis" is just the genitive of "lex", so just like in classical Latin, it means "whether fulfillment of the law is possible". I'm not sure exactly what this is referring to, but if it's for a theological degree it must have something to do with whether or not the Old Testament law can be fulfilled by the events of the New Testament. I'm clearly no expert in medieval philosophy but this looks like the sort of question you would find in Aquinas, for example.

I can help you with resources for medieval Latin though. The ones I learned from are:

John F. Collins, A Primer of Ecclesiastical Latin (Catholic University of America Press, 1985)

F.A.C. Mantello and A.G. Rigg, eds., Medieval Latin: An Introduction and Bibliographical Guide (Catholic University of America Press, 1996)

(Rigg was actually my Latin prof, so that certainly helped me!)

Lewis and Short and the Oxford Latin Dictionary sometimes include medieval usages, but there are also some specialized medieval Latin dictionaries:

Dictionary of Medieval Latin from British Sources (Oxford University Press) - good for non-British sources too!

J.F. Niermeyer, Mediae Latinitatis Lexicon Minus (Brill)

At the best of times it's not much different from classical Latin, although there are a lot of developments that are pretty unexpected at first glance. It's mostly just a matter of semantic changes, and sometimes some Romance-esque grammar. The best is when they use "quod" or "quia" to introduce a relative clause, instead of using an accusative-infinitive construction.