If any regular mode student who has done 1year from ugcrecognised institute, can take admission in 2nd year in LPU online mode?

Yes, LPU does offer offers lateral entry admission to the diploma holders. To join as a lateral entry student you need to write the LPUNEST exam. You can get a seat in LPU if you qualify for the exam. Here is an example of a B Tech CSE admission case.

The eligibility is Pass with 60% aggregate marks in the Diploma 3 years after 10th Or 2 years after 10+2 or B.Sc or BCA or equivalent, subject to qualifying LPUNEST. 

So, all you need to do is merit in LPUNEST!