Institute of Engineering and Technology (IET), Dr. A.P.J. Abdul Kalam Technical University

No, IET for LEET at this rank is not possible. Your rank should be around 10.

Yes, you can get CSE in IET at this rank.

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.

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
Try and maybe you will get in but chances are less.

No chance, but keep an eye on the counselling process and think about some other options as well.

With an OBC rank of 2435 your general rank would be in between 10k-12k (a simple guess), I'm sorry to say with this rank getting into IET is next to impossible so don't hold any false hopes you can get into JSS and here also getting CS and IT would be tough for you.
Getting any other govt college is also difficult and even if you get one you might end up in not so favourable branch.
At last, what I would suggest is that if you have a one more chance in JEE MAINS then go for it because believe me giving another year to study is worth regretting about the college you would be with this rank to make myself clear try avoiding AKTU.