lift stay and evict based on missed June rent.

1.  You can evict as soon as the stay is lifted.   The eviction can be based on unpaid rent BEFORE bankcruptcy filing. 

2.  However, if you want to seek back rent, any unpaid rent before bankcruptcy filing is pre-petition claim, landlord has to "get in line" with other debtors.   So you can wait a long time to see your June rent. 

3. On the other hand, any unpaid rent after bankcruptcy filing can be part of "administrative rent", it means the court will prioritize tenant's asset to pay for his ongoing (i.e. post-petition) living cost first, over other past debt.   This means you might get "first bite" at the tenant's asset for your July and future rent.   However, the "administrative rent" has to be reasonable, so tenant might argue for a lower amount, depend on the circumstances.

In short, "get a lawyer".