Something I have always wondered is how does LA climb standing for extended periods of time. (maybe extreme core strength?)
It all comes down to training for what you want to do. If you prefer to climb in the saddle, then most of your training should involves climbing in the saddle. If you want to be standing a lot, like Lance, the late, great Pantani, Virenque, etc., then you train on climbs out of the saddle.
And yeah, a good deal of core strength and endurance is required. An often-overlooked aspect is form; look at some people climbing out of the saddle and they're all over the place/ Bike swaying a foot and a half with each pedal stroke, upper body moving left and right, weaving back and forth on the road. Think of how much energy they're wasting with all that added movement! When I stand on climbs (which is rare, I spend 90% of any given climb seated) I focus on keeping my upper body very still, keeping the bike's movement to a minimum, etc. It certainly seems to help; when I stand on climbs my heart rate (at the same power level) only goes up by a beat or two per minute.