I like your question - goes at the heart of what the Uni is all about!
I am part of the Production Department, but don't have any other official roles in the Uni. My response here is simply my personal view and in no way an 'official' response to your post.
There are several aspects to 'giving back'. As far as I know, the Uni is doing o.k. financially (in-game and out), including the cost of fueling the structures. Utilising the buyback/lootsheet programme is of course one of the ways in which we contribute isk to the corp, and we get a convenient service out of it in return. Other options are to donate isk and/or in-game items, but that's certainly not expected, just a nice extra for those so inclined.
Then there's the community aspect: the forum, Discord, Mumble, classes, the Wiki, in-game chat, ... Best way to give back is simply be active in as many of these as you can. Specific ways to give back in-game are taking care of skillbook reimbursement requests in the Corp channel and responding to people's questions in the Questions channel.
Other than that, I especially like the idea of just be online in one of the campuses, in the standing fleet and logged into Mumble, and just seeing who else is online and go do something together spur-of-the-moment. When I started out in the Uni, LSC had a number of people who would just hang out on comms, and every once in a while one of us would find a nice juicy target to go hunt after in low-sec. These QRF outings were always a lot of fun. I for one hope to be able to contribute to something like this becoming more active again at LSC.
Thirdly, all of the work going on behind the scenes is done by members volunteering their time and energy. The
Wiki has information on all the different people taking care of their respective tasks like the interviewers, the mentors, the campus managers, the buyback people, etc. And there's a
Forum post that lists the departments with information on whether there are any requirements to joining and whether they are currently looking for more people. Maybe you'll find something where you think, hey, I can do that - and voilà.