Lateral entry

Yes, Anil Neerukonda Institute of Technology and Sciences provide lateral entry for BE in Electrical and Electronics Engineering, for more details check the link below:
https://www.shiksha.com/b-tech/course/b-e-in-electrical-and-electronics-engineering-lateral-entry-anil-neerukonda-institute-of-technology-and-sciences-visakhapatnam-268354

If you wish not to do a job for next 3 to 4 years, you may go for lateral entry. Lots of private engineering colleges are allowing lateral entry for Diploma pass students. However, the best option for a Diploma pass student who is engaged in a job is to do AMIE.
You may get full information on AMIE at the following link:
http://www.amiestudycircle.com

Lateral entry is specifically for Diploma students if you are already pursuing engineering then it will be referred to as a college change.
And college change or university change after the first year is completely dependent on college and university norms, some universities allow it and some won't plus you need to have good scores in the first year to apply for the same. For further details, contact the college authorities.

LEET exam is not conducted by any university as its a state-specific exam.

Amity accepts lateral transfers in only 3rd or 5th semesters.
You need to visit amity.edu and go to the lateral column and fill a form. Otherwise, you can even call the admission department in Amity and they will assist you with the process for lateral transfer of your course.

Amity does accept lateral transfers. Although, there are different rules regarding different courses in Amity for lateral transfers. For more information on lateral transfers, you can contact the admission department.