Hello welcome to careers360.

Well, the LEET or Lateral Entry Entrance Tests are conducted on state level. But some colleges and Univerities too conduct Lateral Entry Tests. You will get direct admission to 2nd year of B.Tech if you clear the exam. Remember, eligibility for admission to Lateral Entry B.Tech course is a minimum aggregate of 60% marks in the Diloma course. 

Now coming to the other part of your question I'll say that no matter which state you belong to, you can try at colleges/Universities in other cities/states; in fact, you can apply anywhere in India. Just visit the websites of different colleges/universities, submit your application and prepare yourself for the Lateral Entry Exam.

Hope this is helpful.

Good luck!