Lift if the other lane breaks?

No rule on the run it out other than maybe the safety of the other car/driver. If the car broke and was still up the track in their lane, etc. If they are at the line, run however you like. EWliminations, keep inmind, if they don't redlight him to let you loose, you can't break out. If they are staged don't redlight yourself or breakout.

Courtesy staging is common. Some cars need a bit of time to get from pre stage to stage. If you double bulb them, the timer starts and will redlight them if they aren't staged after 8 seconds, IIRC. That's the only deal with courtesy staging.
At my local tracks (not sure about everywhere), the clock doesn't start until it see's 3 sets of bulbs. In other words, if someone rolls right in and double bulbs me I can take all afternoon to stage the car, but as soon as I light the pre-stage bulb (the third set of bulbs the starter sees) the timer starts. My local tracks have anywhere from 7-10 seconds at that time.

Also fun side note (because I get a mean streak sometimes), if anyone double bulbs me....I'm on e85....I will literally wait for over a minute and watch them get pissed off while my car is nice and cool (thank you e85)....then when I think they have had enough fun I stage. This pretty much guarantee's a win, because the other guy will be all worked up and mad by that point...and they can only blame themselves for not courtesy staging.