Hey

No, you cannot pursue a 3 year LLB course from any NLU. You can get admission in NLUs through CLAT which provides admission only into a 5 year Integrated course of law which combines an Undergraduate degree with law, for example- BA LLb, BCOM LLb, BBA LLb etc. NLUs dont provide 3 year law courses.

As you have completed  graduation in bcom a 3 year LLb degree is more suitable for you. You can apply for admission to a 3 year LLb course while you are in your final year or after completion.

Your admission will be based on your score in the entrance tests. There is no common entrance, each college has its own entrance. Few of the entrances for a 3 year law course are- 

DU LLb- Delhi University 

MH CET- GLC Mumbai, ILS Pune and other law colleges in Maharashtra  PU LLB- Panjab University,Chandigarg

TS LAWCET- Law colleges in Tamil Nadu

BHU LLB- Banaras Hindu University.

BVP LLB- Bharatiya Vidyapeeth University

 LSAT- Private Law colleges like O.P. Jindal Global Law school, IIT Kharagpur etc

You can apply for these  and you'd be eligible to take admission only if you score the minimum qualifying percentage in your UG degree which is usually 45-50%.

You can use the link below for any other information.

Https://law.careers360.com/articles/9564-law-entrance-tests/amp

Best of luck