She can sign at any time; six months in MA

If you tell her in April to move out in May, she could immediately sign the lease.  At this point you should treat lease as signed, unless you can prove in court that lease was not signed when you tell her to move out.   Can you get the unsigned lease back under certain pretense BEFORE you tell her to move out?  If not, assume the lease is signed. 

Here is mass law:

http://www.masslegalhelp.org/when-is-eviction-illegal

If a landlord tries to evict you or sends you an eviction notice, a rent increase notice, or a notice of any substantial changes in the terms of your lease or tenancy within six months of your having engaged in any of the activities listed above, a court must "presume" that the landlord is retaliating against you.