Lactic acid doesn't cause muscle soreness the next day
For decades, delayed-onset muscle soreness was explained as lactic acid building up in the muscles during a workout and supposedly getting 'stuck' in tissue, continuing to cause pain for a day or two afterward. Physiology fully disproves this mechanism: lactate produced during intense muscle work clears out of muscle tissue and fully normalizes in the blood within roughly an hour after a workout ends — long before soreness even begins to show up.
The real cause of delayed muscle soreness, which usually builds over 12–24 hours and peaks around 24–72 hours later, is micro-damage to muscle fibers and connective tissue from unfamiliar load, followed by a local inflammatory response that produces the soreness as the tissue repairs. That's a fundamentally different process, unfolding over days rather than the hour or so it takes lactate to clear.
The myth stuck around partly because both phenomena — the burn during a set from lactate, and the pain the next day from micro-damage — subjectively feel like 'muscle pain,' even though they're two completely different physiological processes with different causes and different timelines.