Two possible developments:
1. landlord, I need the signed lease back, tenant: okay, here it is, signed.
2. landlord, I need the signed lease back, tenant: (silence or BS or no action); landlord, I asked the second time, I need the signed lease back; tenant: (silence or BS or no action). Landlord, sending a registered letter saying he needed the lease, or he would treat it as unsigned and the tenancy is month-to-month.
Tenant: (silence, BS or no action), Landlord can send notice to end tenancy.
I don't think tenant will return the unsigned lease. But if she did, congrats.