Your sensor or switch will need power. You can power it with a (second hand) 5 volt phone charger plugged directly into the Arduino Nano. We like the IKEA chargers.

The SMS modem in the door lock will need a power supply that can deliver at least 2 amps.

If you have them, you can also use 9 or 12 volt power supplies which use the round 'barrel plug' connectors.

Wireless connection problems are often the result of using poor quality power supplies. These create a lot of 'noise' which affects the radio components.