Yes, you can join NLSIU after completing B.Tech degree. The university gives admission to a 5-year integrated program that is BA LLB. The basic qualification required is 10+2.
Since you have already completed the B.Tech program that is of 4-years after 10+2, if you do not have any issue completing a five-year program, then apply for CLAT and appear in it. Of course, it will be easy for you to appear in CLAT as you are an IIT student.
However, you should make sure to check the notification on the official website of the college before applying.