How does everyone take care of dead skin cells on their lips?

I am someone who suffers from dry, flaky lips all year round.
Especially in dry weather like this, my lips get even more chapped and cracked, so I'm really worried.

Do you happen to have your own secret tip for soothing dry, flaky lips at home without irritation?
Recommendations for 'holy grail lip balms' or 'lip masks' that leave your lips smooth the next day if you apply a generous amount overnight are also good,
If you have a specific routine for soaking and removing it while showering, please be sure to share it.
I want smooth lips too.
I look forward to advice from the experts!