What is the ruling on a married man kissing a woman who is unlawful for him out of lust, and what is its evidence from the Quran and Sunnah, and what is the recompense for its doer in this world and the Hereafter?

What this man did is forbidden and a step from the steps of Satan. Allah has commanded to lower the gaze and guard one's chastity. It is narrated in the Hadith (definition) that "For one of you to be stabbed in the head with an iron needle is better for him than that he should touch a woman who is not lawful for him." The worldly punishment for this is discretionary chastisement (ta'zeer), and its perpetrator should conceal it. In the Hereafter, he is exposed to Allah's punishment unless he repents. He must hasten to sincere repentance and perform the obligatory duties, for good deeds erase bad deeds.