Control 12v lock switcher with Arduino Nano
A definite answer isn't possible without more information about the lock.  You likely want something like this:







simulate this circuit &ndash; Schematic created using CircuitLab

Drive IOPIN HIGH to ground the PUSH pin.

Many other parts could be used in place of the IRLML2502. It's convenient for driving directly from an IO pin. Whether you need the flyback diode D1 depends on the lock.