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This may be a rookie question:

Many 1L summer internship applications require a reference list of 3 contacts. I’m going to include 1 from former boss (I worked with him in between undergrad and law school), 1 law professor, and 1 undergrad professor (my thesis advisor, my mentor from undergrad).

Would it be okay to write in an undergrad professor for reference list?

You should really find another law prof or law-related reference if you can. But it’s not likely to make any real difference - very few 1L jobs are going to contact references.

It's absolutely okay and borderline expected. Hell, I had 2 undergraduate professors and 1 law school professor and I don't think any of them were even contacted.