How necessary is a List of Figures and a List of Tables in a dissertation?
To be honest, with a short dissertation with only a few figures and tables, it probably doesn't really matter one way or the other.

If your institution's dissertation guidelines say anything about it, follow them.  If not, I'd say just include the lists, unless you feel you have some good reason not to.  In which case, don't.  Your advisor should let you know if they believe such lists should be added or removed, anyway.

Or you could just ask your advisor about it to begin with.