Why did the backup landing gear deployment fail on LOT 16?
Gravity/freefall backup (or more precisely some backup) is mandatory, but in large aircraft running pulley from cockpit to the wheel wells to release the uplock (the thing that keeps the gear retracted) mechanically would be too complicated or the force required to operate it too large, so the uplock still needs to be released electrically.

Unfortunately the circuit breaker that protects the circuit responsible for releasing the uplock was "popped" (open), so the uplocks didn't release and the gear didn't fall down.

The crew was trying to troubleshoot the issue for 80 minutes and consulted maintenance over radio, but because the checklists for either central hydraulic system (which does the normal gear extension) failure or alternate gear extension did not mention the circuit breaker (C829) neither crew nor maintenance thought of checking it.

It is not possible to find why and when the breaker popped. They tested the alternate extension afterwards and it worked, but the breaker covers several other circuits and there could have been transient problem somewhere or it could have been maintenance error or some other reasons.

You can read excerpt from the report on The Aviation Herald.