The way I see it, there are four options:

1. Set your alarm to vibrate, sneak to the other room.
2. Don't try to LD when your girlfriend is over (unless you live together!).
3. Get a girlfriend that enjoys lucid dreaming as much as you.
4. Slip a sedative into her drink. Just kidding! (Seriously. Don't do it.)

Joking aside, give those first two a try. She should accept your sleeping habits, and you should accept her wishes not to be awakened at unsightly hours via alarm. Relationships are about mutuality. Good luck!