No, there is no option of lateral entry in BIT Mesra, especially for engineering. For other branches, there may be depending on their selection criteria.
BIT Mesra admits students in its B.Tech/BE (Engineering) programs through JEE-MAIN-CSAB route. There may be some special spot round of admission through CSAB, but they do not conduct any lateral entry procedure of their own. Even if there is any number of seats that lay vacant (which usually is the case), they don’t conduct a lateral entry of their own.
So, in a nutshell, study hard for your JEE MAIN if you want to get into the BIT Mesra B.Tech/BE program, as this the only route of entry into the institute.