You'll never be 100% a few hours after exercise, but if it's not too stringent you can get damn close.
As for heavy lifting, that varies depending on the kind of program you're doing, how conditioned you are and how hard you're going in the workout. Olympic athletes train the same muscle group 5-6 times a week. Beginner powerlifters can get told to put a day of rest between each workout, or even two. Properly damaged muscles do take a few days to fully repair though - this doesn't mean you can't use them again or that you shouldn't lift until you're 100% again. But you do need to be wary that they are getting enough recovery or you could enter overtraining mode and, whilst not a fatal thing, it can certainly hinder your process when your muscles don't have the adequate rest to rebuild, which is why we damage them in the gym in the first place.
So I would gauge it and experiment with your own body and muscle groups. DOMS isn't always a good way to judge if your muscles are ready to tackle a workload again. As an example, I was training only twice a week until recently and had consistent doms all the time - I thought I'll wait until I don't have doms this frequently before I go adding a third session in. But the doms didn't disappear, so I said fk it I'll just train with sore legs - I lifted more in that session than I did in my regular session, and since doing 3 a week I no longer have doms as bad. Go figure. I may have been resting too much and was out of condition. There's probably an exact science behind all that, but regardless, I say experiment yourself with recovery, because everyone is different. But yes, muscles need days to properly heal 100% from heavy lifting and recovery from sport or non-resistance training should be a lot quicker for muscles as it doesn't appear to damage muscle as much as it does joints (keep an eye on joints for repetitive strain injuries).