Hello Aspirant

I'm assuming by BE you mean Bachelor in Engineering. In this case, yes, you are eligible to become a lecturer at a polytechnic college.

The eligibility criteria for a lecturer, in engineering, are that the candidate must have a valid degree from a UGC-recognised college/university. They must have cleared the UGC-NET exam in the field of  Engineering. For good institutions, they even ask for a PhD and a good number of experiences.

Hope this helps