Which math departments in the U.S. have people known for their contributions to Lie-admissible algebras?
You can try searching for "Lie admissible algebra" on MathSciNet and the arXiv.  There are a few papers each year that mention this topic, but it doesn't seem to be a major research area in its own right.  If you are thinking about topics for graduate school, this seems to me to be way too specific to narrow down to before choosing an advisor.  (I assume you aren't already working in this research area yourself: if you did, you'd have more information about who else is.)

As for math departments in the U.S., two of the authors of references in the article you linked to (Benkart and Osborn) are emeritus professors at Wisconsin, and Myung used to be at Northern Iowa but has since died.  You could try looking up the authors of papers on the topic that excite you, but this won't give you a wide range of schools in the U.S., especially now that Benkart and Osborn have retired.  Instead, I agree with Chris C that you'd be better off considering a broader area.