anywho i was 20 when i started dating my gf who was 17, and then i turned 21. if her parents are cool with it then its not a problem. Age is always just a number, its about maturity levels here kiddies.
Anywho its been over a year and im still with the same girl so it is possible you could be with her for awhile, no need to lie. Just say you are 20 and when your 17 year old told her parents you were 19 she was mistaken.