Am I eligible to pursue LL.B. with 59% in B.Sc?

Yes, of course. There is no such restriction. Only thing is to clear the entrance test. 50% marks in graduation is enough for a decent institute.

Hi, LLB Eligibility. Aspiring candidates should have scored a minimum pass percentage either at the class 12th level or graduation level. The percentages are 45% marks for General category, 42% for OBC and 40% for SC/ST categories.