<p>You can’t do it concurrently.
You could conceivably work part time after college, get a Master’s after your BA in CS either being sponsored by your employer or part time, and after 5 years of work experience and two CS degrees be a very competitive applicant for Law School - keeping in mind you’ll need to find a flexible college where you can do a CS major AND a humanities or social science major.minor or at least a variety of classes. (While you can apply with just a CS degree, Law Schools will expect you to have taken a couple classes in philosophy/history/political science/economics and, probably, English/foreign languages&literature.)
Graduate school or professional school is like a job - a very intense, time-intensive job. You question is similar to “can I be an investment banker and an engineer at the same time?” There just aren’t enough hours in the day.</p>