Q: Can I put a lock on my printer while using AirPrint? (similar to locking on Apple TV on the same Wi-Fi network)

Read the documentation that came with the printer since your question has nothing to do with your phone.

You don't necessarily need a printer that supports AirPrint

You can use any printer and install AirPrint enabling software on a computer connected to your printer

There are free and paid versions of AirPrint enabling software

The computer that is running the AirPrint software has to be on 24/7

http://www.ecamm.com/mac/printopia/

You can also use a raspberry pi , a credit card sized, low power consumption, cheap Linux computer

As a AirPrint print server

http://likeaboss001.wordpress.com/2013/04/21/raspberry-pi-airprint-server-how-to /