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

The cut-off depends upon the various factors like difficulty level of the UPSEE 2018 entrance exam, Past years Cutoff trends, Total number of participating institutes, Total Number of seats available, Total number of candidates who cleared the UPSEE exam and the total Number of candidates who appeared for the entrance exam. The previous years cut off will helpful in your case.
# In 2015, the opening and closing ranks are 1639 and 1841.(OBC girl)
# In 2016, the opening and closing ranks are 1736 and 2659 (OBC girl)
# In 2017, the opening and closing ranks are 1110 and 1548 (OBC)
Good luck.

No, you can't get admission in IET through lateral entry.

No, on the basis of your general rank, you can't get IET.

Kindly specify the entrance exam name.

No, with this rank for lateral entry, you'll not get any government college, but probably you can good private colleges like:
Galgotias University
BBD
SRGI
Ajay Kumar Garg Engineering College

Yes, on the basis of your rank, you can get IET, Lucknow for:
COMPUTER SC. & ENGG. (SHIFT-I)
ELECTRONICS & COMMUNICATION ENGG. (SHIFT-I)
INFORMATION TECHNOLOGY (SHIFT-I)
ELECTRICAL ENGG. (SHIFT-I)
ELECTRONICS & INSTRUMENTATION ENGG. (SHIFT-I)
MECHANICAL ENGG. (SHIFT-I)
CHEMICAL ENGG. (SHIFT-I)
CIVIL ENGG. (SHIFT-I).

Yes, of course. There are good chances for you to get ECE in IET, Lucknow.

Yes, you can get admission.

Hello,
I hope you are doing well. You can check the list of colleges including NITs and IIITs that you can get according to your marks and rank. Use Shiksha JEE college predictor:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=connect&utm_medium=CR_JEECP&utm_campaign=7489993.

There is no chance in Mechanical engg in IET and BIET.