I agree with Klaus. The nodeMCU has a linear regulator on board and the "Vin" pin has a diode in series with it which already drops about 0.5V, if you start with 4.35V then lose that 0.5V you only have 3.85 left to feed the 3.3V regulator, it isn't enough.
Does the lock operate if you short out the contacts on the relay? I mean linking them as though the relay had operated. The lock release on my gates at home needs 2A at 12V so you may need more power for that as well.
Brian.