L1 is going to expire H1 Petition received

Hi, I am currently on L1 which is expiring on August 05th. Applied for H1 Visa and got selected in lottery. My Employer told like he is not going to apply for L1 extension. What is the way to handle my stay in US after the expration date of L1.

There is no other way around, you will go out of status if you stay in USA after that. So, you will have to go back to your home country and get your H1b stamped to return back for the Oct 1st start date.