I was in a similar boat and applied this cycle. I am currently in my postdoc, and got 1 LoR from my postdoc advisor, 1 from my graduate advisor, 1 from another research professor in my postdoc lab, and 1 from a volunteer manager.
You don't need undergrad (unless it is a very, very specific requirement). For instance, many want a LoR from someone who taught you science. While this is normally an undergrad science professor, your thesis adviser would know you much better than your O Chem professor from a 100 person class, ten years ago. I got an interview at Rush, and they had very particular LoR requirements, but I was able to assign the letters for each specific requirement (i.e. they wanted a 'personal' letter, which was one from a research professor I work close with, even though that letter could also have been used for research purposes).