How to drill a hole near a wire in a wall?
Use the depth of the plaster/lath; say it's 5/8". 


Put a piece of tape around the drill bit at 5/8" to ensure you don't drill deeper. 
Drill the surface hole 5/8" deep. 
Once the surface hole is made, you can turn on the electricity and insert a non-contact inductive wire sniffer (like this one from Fluke: https://www.amazon.com/Meterk-Non-Contact-12V-1000V-Flashlight-Multi-sensor/dp/B0711KGPYD). 


Note this will only detect the "hot" line (not ground).