#after himself

"behind him" or "after he went through"

#I beg you, my brothers

"I plead with you, my brothers"

#my brothers

Lot spoke in a friendly way to the men of the city hoping that they would listen to him. AT: "my friends." (See: [[:en:ta:vol1:translate:figs_idiom]])

#do not act so wickedly

"do not do something so wicked" or "do not do such a wicked thing"

#Look

"Pay attention" or "Look here"

#have not slept with

Your language may have a way of saying this politely. Some older versions say "have not known." (See: [[:en:ta:vol2:translate:figs_euphemism]])

#whatever is good in your eyes

"whatever you desire" or "whatever you think is right"

#under the shadow of my roof

The two men were guests in Lot's home, so he needed to protect them. The word "roof" is a synecdoche for the whole house and a metaphor for Lot protecting them. AT: "into my house, and God expects me to protect them" (See: [[:en:ta:vol2:translate:figs_synecdoche]] and [[:en:ta:vol1:translate:figs_metaphor]])