Sorry to say this idea got put on the backburner for me. I've got nothing to contribute to.

Luckily, WebWork has got something working. Have a look at the documentation for their LTI-Advanced Authentication. For working code, you'll have to got to their Github repository because no one has uploaded an LTI module to CPAN yet. This might get you started (or drop you off in the deep end).

And there are blogs (recent) and forums (not so recent) where you can catch up with the current state of LTI and Perl. Get up to speed and then check out the mailing lists.

Best of luck in dipping your toes. If you hit a brick wall, I might be able to carve out some time to work on a specific problem. Reply to this post and I'll see it next time I log in (which could be next week or could be September)

(Edit) Latest version of WebWork has a couple of issues that add features to some LTI links.