In all honesty I am not sure if admissions committees really even look at LOR's, personal statement etc. I remember stressing out about those when I was applying, but in the end my numbers got me into the schools I expected to get into. If you look at lawschoolnumbers that seems to apply to all applicants and admissions decisions seem to be based on nothing more than your LSAT/UGPA. Schools do claim to put considerable weight into LORs and personal statements, but I wonder if they even look at those materials.
In response to your question 3 letters is good and if you have more that is great to. All schools have a maximum number of recommendations they will accept and I would imagine it is best to submit the maximum amount of LORs if they are from reasonable sources. Regarding the recommender you specifically mentioned he probably would not be a great reference since you never worked for him or had in him class, but as I said it seems unlikely a school will put much weight on the LOR.