Yes, because there's more than one way to skin a cat, and more than one way to train for the 800.
You need to take into consideration your own talent. Are you a 400/800 guy or an 800/1500 guy? The former focuses on speed endurance training and the latter on aerobic strength, but both touch on all of it.
If I tell you what I do (I was 2:03 at the age of 16 and 1:53 now) that would be just one more differing opinion.
Lift if it helps you. To test how if it helps you, ask yourself, "am I strong?" If the answer is no, lift.
Run 25-60 miles a week. The less miles you run, the greater the percentage of it has to be at or faster than race pace.
Speed, speed endurance, lactic threshold, vo2max. Understand these first three terms (and the fourth one if you're a 800/1500 guy) and incorporate the into workouts - aiming to isolate 3 of them every week and never ignoring one for very long.