I'm not sure how far in advance they take reservations but you can email them or call. It's almost like booking a private party. You tell them how many in your party and what date and time and they send you a "contract" to sign. It's been over a year since we have used priority bowling.
Christmas time might be more crowded but if you are going during the day generally you can get a lane pretty quick, at night is when they get really busy. We were there on Jan 1st around 6pm and had to wait about an hour for a lane. A table was available so we ate first and as we were getting done a lane came available. We are going in June and have an ADR booked at 6:30pm so we will request a lane when we get there and wait if we need too. If you definitely want a lane and don't mind the extra cost then I would go the priority bowling route. This is what we did for the 2 times we went on Christmas Day.
You can also eat while you bowl which is what we have done every time we have done priority bowling but a few in our group get a little freaked out about germs(think bowling balls and hands) so we have decided to eat first then bowl this time.
Splitsville has become a must do for us.