Seeing as they had just appointed Lot a judge (Rashi to 19:1), how could they now accuse him of judging them?
Keli Yakar, Taz: The judges of Sedom were not conventional judges, who sought the truth and acted upon it. They judged by the evil, cruel laws of Sedom. In fact, Lot's defense of his guests clashed head-on with the pervert laws of Sedom, which were designed to strip the visitor of his money, his dignity, and even his life, if it suited them. 1
As Eliezer Eved Avraham discovered when he visited Sedom, as related in the Midrash.
On what grounds would the menof S?dom now treat Lot worse than his guests?
Oznayim la?Torah: Because a. he was a newcomer who had been lax in learning the local laws and customes, and b. for having the audacity to accept the position of chief judge of S?dom when he disputes their laws.
Seeing as the word "va'Yiftzeru" has connotations of appeasement, what were the people asking Lot here?
Ramban: Either to open the door to let them in, or to move aside and give them access to enter.
Why does it say, "They said... they said..."?
Moshav Zekenim: They said "Gesh Hal'ah" to words that they were pleased to hear (do to my daughters as you wish), and they said "one came to live - will he judge...?!" to words that they did not like hearing (do not harm these men). 1
Hadar Zekenim and Riva say similarly.
QUESTIONS ON RASHI
Rashi writes: "Regarding the daughters, they said, 'Get out of the way!' Regarding his protecting the guests, they said 'Has one man come to sojourn, and he judges and rebukes us?" How do we know do divide their words in such a manner?
Gur Aryeh: "Get out of the way" (Gesh Hal'ah) sounds like they have no wish to talk to Lot, yet they continued talking! Rashi explains that they comprise two separate reactions to two requests by Lot.
