It increase the amount you are applying to the principal on the following payment threrefore reducing the outstanding principal balance. So there is a 1 pay lag time.

No it doesn't.  Test it.   I tested it with my lender (Wells Fargo) and it makes no difference.  

It also makes no difference if you pay your mortgage early (for example pay December's payment in October).    Since I pay electronically, I schedule the payment only a couple of days before it's absolutely due (generally the 15th).  

Please test it with your lender and report back.  

(I'm talking about timing of mortgage payments here, NOT making any additional principal payments).