“my lords.” This is the use of “lord” as a customary greeting of respect, like we would say, “Sir,” when we do not know the person.

“city square.” The open place associated with the gate complex of the city, if the city was a walled city, which Sodom was since it had a gate. It would be customary for these strangers to not accept such an invitation immediately, but to wait until they were pressed upon to accept.