Is there a way to get actually kicked out of university?

Seems like being suspended is as far as it goes. Once your sim can enroll again, if they get suspended again, the suspension will be longer.

But yeah. You know...
Dropping out is always an option...

Unless I'm confusing it with Sim3, I thought there was a way to drop out.

Thanks guys! I know you can drop out I just wanted to see if you could get thrown out, just to see what would happen haha. Also it goes with the downward spiral I wanted Lilith to have

Yes...
The thing about dropping out is that it erases all the progress you've made. So if your sim drops out and reenrolls, they start again from zero.
Suspension and withdrawing from term will keep the progress.

Just a fun fact.

This happened to one sim I was playing, Bastien. He was in a group of students so I wasn't playing him on his own. He was on the soccer/football team but while the others would pass, he kept bombing the grades in his classes despite doing the work. Each semester he fell further behind. Finally he went on academic probation and then did not achieve the necessary grades to continue. Rather than re-enroll, I concluded that it was time for him to join the workforce. He was from a wealthy family with a father in business who wasn't that happy about the continued failures.

That's not the norm, sims usually have great grades or might hit a bump but recover. He actually failed out. On the other hand, he stayed in shape but I think Daddy got him a start in the mailroom.