All you need to do is call 311. If you do it like the day prior to pickup they normally have it repaired or replaced by the day after pickup. If it is something they can repair on the spot they will just repair it. I had to get a new lid after the truck broke the clips on my can during the dump.
311 will tell you to leave the can curbside until it is repaired. Codes will see the can is damaged and should not write you up or ticket you for not having the can off the curb by midnight pickup day.
If it really was out for repair and you get in trouble by codes they can just go back and check in the system that a repair order was requested.
