Colleges in Lucknow

You have to give the entrance examination (UPSEE).

These are some of the best government colleges:
Institute of Engineering and Technology, Lucknow
Madan Mohan Malaviya University of Technology, Gorakhpur
Kamla Nehru Institute of Technology, Sultanpur
Bundelkhand Institute of Engineering and Technology, Jhansi
University Institute of Engineering and Technology CSJMU, Kanpur
Dr. Ambedkar Institute of Technology for Handicapped, Kanpur
Nitra Technical Campus, Ghaziabad
Feroze Gandhi Institute of Engineering and Technology, Raebareli
Government Engineering College, Banda.

No, it can't be regarded as NITs. However it can be said to equivalent to some of the very new NITs, that to in near future. However NITs are the top and Apex of JEE Mains.

It's a private college. You need to qualify MAT, CMAT or ATMA to get into it.

No, at this rank, you'll not get lateral entry because lateral entry depends on the basis of vacant seats in second year and you have a very high rank for lateral entry. Iin IET, your rank should be around 10.

IET Lucknow seat matrix:
Total seats for 4- year B-Tech 480
Chemical Engineering 60
Civil Engineering 60
Computer Science and Engineering 60 Electrical Engineering 60
Electronics & Communication Engineering 60
Electronics & Instrumentation Engineering 60
Information Technology 60
Mechanical Engineering 60
You may easily get in but the branch may not be the same as you want.