BE 1st year discontinued students eligible for lateral entry admission.
Nope! For lateral entry examinations only those who have pursued the Diploma in Engineering are only eligible. Now for the BE/BTech courses most universities ask to complete the course in 6 years time period from the year of admission. So you get 2 years in excess to clear backlogs or other things. I would recommend you to visit the college and get the information if you can continue the course further or else you have to take admission from the 1st year again.
To know more about Engineering visit the link below:
https://www.careers360.com/courses/engineering-course
I hope this answer helps. All the very best for your future endeavors!