1. I ask because it sounds like the voltage dips enough when the electric lock is energized to cause a restart of the other device.
2. Just to be sure I would check ratings for the device from a label or part number.
3. When an energized coil is de-energized it can generate a big and backward voltage spike that can damage a semiconductor output. The diode is placed across the coil with its cathode (the white band) to the positive side of the DC coil to clamp that voltage and protect the output driver. It can also be incorporated inside the device where it's not visible.
It's likely that the manufacturer took this into consideration and the output is protected. It may also be a "dry" relay closure output which can negate the need for a diode clamp. I cannot say for sure, not having the installation instructions / user manual.
Does the manual have info regarding the electric strike, such as its operating voltage and if it requires an external 12VDC or 24VAC power supply to operate the lock / strike?