We recently gave a 30 days notice to our landlord that we wanted to move out at the end of a one year lease and gave her a specific date. She responded and said that would be fine. Now however, it has been discovered that the lease actually adds on one year plus 25 days. Now she's saying she wants the extra 25 days rent plus she's going to keep the security deposit since we are moving out before the lease is up. Is this legal? Can she make it one year plus 25 days?

A lease can run for whatever length is specified in the lease. What was the start date of the lease and when does it end. She can make a lease longer than a year, she can charge you for an extra 25 days if you really have a lease that is 1 year plus 25 days but SHE CAN NOT keep your deposit too.

The lease is for the specific time listed in the lease,
It should say the exact term, from date to date.
Also. Many renew automatically
Also. Most require 60 days notice not 30.
But that would be in your lease