I'm going to completely disagree here.
Elite level decathletes run 40-50km weekly mileage (most of it very fast) and are still able to put up 500# squats, 300# cleans, and 15m shot puts. Some beyond that.
The body systems don't work against each other. The reason it's hard to do both is because you need to be put in the time and effort to train both, and you need to have superior recovery ability so that you can recover from both.
Anaerobic exercise does not increase aerobic capacity. That's just silly. Anaerobic training can help in aerobic sports, but that's different.
Lactic acid is removed from the body almost immediately after exercise. It's not in the muscles on off days, so there is no reason for that.