Correct date for sending tenant notice of lease termination?

[Noureen A S.]

(note: I meant to post this the local North Carolina RE forum)

I've decided to terminate my tenant's lease. They've given me a few signs that they're not going to be able to keep up with rent over their next (year) term. 

Their lease actually ends March 15th. As per the NC statute concerning lease terminations, I should have sent them a termination notice ("notice to quit"?) by February 15th (or around that date since Feb had 29 days).

Its now March 2nd.

And now that my timing is off, I'm confused about what will happen to their lease end/move-out date: I had to give them 30 days notice before the end of the lease and not having done so will cause them to occupy the unit past their original lease end date (March 15th).

Additionally, if I understand the wording of my lease correctly, if tenant remains in unit after lease ends and without renewing the lease, the "lease" defaults to a month to month...

Exact timeline for everything is clearly confusing to me since I missed the date for sending a lease-termination notice... 

Just trying to cover all bases (while overthinking at the same time)... Do I just send termination notice ASAP and make their lease-end date 30 days from the date of the notice?

Thanks in advance.