Here are my data points for receiving the 20% or 30% bonus:

1/29: I crossed the 100,000-LP threshold.
2/9: I had a stay from 2/3 - 2/6 post with a 20% LP bonus. (I booked the stay on 2/2, which is after I had crossed the 100,000-LP threshold.)
2/11: I received the e-mail from AA about hitting 100,000 LPs.
2/13: I had a stay from 2/8 - 2/10 post with a 20% LP bonus. (I booked the stay after I had crossed the 100,000-LP threshold but before I received the e-mail from AA.)
2/17: I had a stay from 2/10 - 2/14 post with a 30% LP bonus. (I booked the stay after I had crossed the 100,000-LP threshold but before I received the e-mail from AA.)

From the above, my best guess is that as long as the stay ends after you receive the e-mail from AA, you should receive the 30% LP bonus. It shouldn't matter when you actually book the stay.

To corroborate this, a fellow FlyerTalk member informed me that he received a 30% LP bonus for stays that he had booked before crossing the thresholds but occurring after receiving the e-mail from AA.