When should the lips be washed during ablution (wudu')? Is it during the washing of the face or during rinsing the mouth (madmadah)? What is the evidence for this? And what is the ruling for one who did not specifically do anything for them in their ablution?

The outer part of the lips is considered part of the face, and it is obligatory to wash them during ablution along with the rest of the face. There is no specific wash required for them. Therefore, whoever did not wash the outer part of their lips in general, their ablution is invalid, and their prayer performed with it is null according to the majority of scholars. They must repeat the missed prayers, and if they do not know their number, they should exert effort and repeat what they most likely believe to be their number. Sheikh al-Islam Ibn Taymiyyah held the view that whoever omitted washing them out of ignorance of the ruling, must repeat the prayer of that time and adhere to it in the future, but is not obliged to repeat what has passed.