Top Law Schools

I am applying to law school for this upcoming fall, and I have noticed that some law school have law informatics research labs (such as CodeX at Stanford, the Legal Information Institute at Cornell and labs at Michigan St. and Hofstra) and some faculty at a few law schools do research in Legal Informatics (Daniel Katz at IIt Chicago-Kent, Harry Surden at Colorado and Kevin Ashley at Pitt). Though my goal is to go into IP law, I do have an interest in informatics (I have an MS and soon will complete my PhD in BioMedical Informatics), and I am especially interested applications for natural language processing with legal text.

I understand that law school is primarily a trade school, but if I go to a school with a research lab, or a faculty member doing research in this field, is research or joining the lab a realistic possibility? What is the relationship between these types of labs with their law school? Is there any reason to prioritize schools doing this type of research over others? and should I try to contact the faculty doing this work for more information, or is that frowned upon if I am applying to the school?

1. employment outcomes >>>> everything [though the extent to which this feeds back into a potential employment outcome is something i can't imagine many people, myself included, can grasp]
2. many people, myself included, have "broken ties" between opportunities presenting roughly equivalent employment outcomes [or approximately equivalent employment risk : cost ratios] for much stupider reasons than the one you propose here, especially given your background
3. i see no reason a professionally and politely phrased communication to individual teachers would be inappropriate just because you are also applying to the school. but if you are worried about it, you can let the applications fall where they may and ask the admissions offices that accepted you to put you in touch with the relevant people afterward. i'd probably reach out first, because what the hell why not if it's executed correctly it's got more upside than downside.

as an aside, i'm not much of a careful-you'll-get-outed!! fearmonger, but in all likelihood you're going to be extremely easy for schools to identify on here. it goes without saying that this post and future thoughtful ones like it are totally fine.