For me, lactate buildup shows as temporary muscles burning, fatigue is swollen, heavy/failing legs with falling power, and soreness is soreness, and I honestly don’t recall feeling muscle soreness on the bike too much, except maybe some soreness (lactate?) from yesterday’s riding.
eta- You can keep pushing over threshold, like if you’re in the middle of an interval, but you’ll only be able to do it so long. Then you ease up the intensity because it’s the end of the interval or you’ve crested the top of the hill or you want the pain to go away, and your legs will recover so you can do it again if needed. (You didn’t really provide a specific scenario)