Forgot broken iPhone's lock screen password.

Normally, no. Because the phone would be erased as part of the repair process. So, normally when you get a repaired phone back it will need to be set up again, just like it was a new phone.

For example, my wife dropped her phone and the phone would not work correctly. The phone was repaired at the shop. When we powered up the phone again, the phone displayed the "hello" screen and we had to set up the phone again. We could have used the old passcode if we wanted or set up a new passcode.

When the phone is repaired, it will look like a new phone, so you will need to set it up again with a new passcode.

It's really old fashioned, but it just might be a good idea to write down the new passcode and keep it in a safe place......even if you are sure that you will never forget it.