Can graduate students who don’t have to pay tuition but had other fees still apply for a lifetime learning credit? Without a 1098-T?

Yes, if you have qualified education expenses for the Lifetime Learning Credit, your school is eligible education institution, and you could get the school's Employer Identification Number. 

• An eligible educational institution is a school offering higher education beyond high school. It is any college, university, vocational school, or other post secondary educational institution eligible to participate in a student aid program run by the U.S. Department of Education.

Here's how to visit the Education section:

1. Open (continue) your return, if you don't already have it open.
2. Search for 1098t and then select the "Jump to" link or "Go to" button at the top of your search results.
3. On the Did you get a 1098-T for the year 2019? screen, answer No.
4. On the Ok, Let's see if you qualify for an exception screen, make a selection. 
5. Continue with the onscreen interview until complete.