Hey Sanajit.

No, you cannot do 3 year LLB course from any NLU/ national Law Universities. All the NLUs in India offer only 5 year integrated law courses which combine an undergraduate degree like BA, BCOM etc with Law. This course is appropriate if you want to take admission in law after 12th class directly.

If You wish to take admission in law after completion of any graduation degree separately, then you can go for 3 year LLB. There are colleges other than NLUs that offer 3 year LLB.

Here is a list of law entrances for 3 year LLB course -

 DU LLB - Delhi University

MH CET- GLC mumbai, ILS Pune and other colleges in Maharashtra

SLAT- Symbiosis Law school

PU LLB- Panjab University, Chandigarh

LSAT- Jindal global Law school, IIT Kharagpur and other private law colleges

BHU LLB- Banaras Hindu University 

BVP LLB- Bharatiya Vidyapeeth

TS LAWCET Etc

Best of luck!