Muscle soreness isn't caused by lactic acid.
Lactic acid is cleared within about an hour after exercise. Delayed soreness, however, starts only 12 to 24 hours later and peaks at 24 to 72 hours. The cause is tiny tears in the muscle fibres and the inflammatory response that follows. Braking movements such as downhill running hit hardest, because the fibres are stretched under load.
Useful: After the first bout, the muscle protects itself: the same load weeks later barely hurts.
Source: en.wikipedia.org