I use my MacBook Pro with an LG monitor, and the MacBook is always plugged in. Does that reduce battery life?

I would recommend turning on Optimized battery charging in System Preferences. It will keep the battery at about 80%. See the information in Charge the MacBook Pro battery - Apple Support including the following:

• Optimized Battery Charging: This feature helps to reduce the wear on your battery and improve its lifespan by learning your daily charging routine. It delays charging the battery past 80% when it predicts that you’ll be plugged in for an extended period of time, and aims to charge the battery before you unplug. You can change this option in Battery preferences.

rallenk wrote:

Is battery life reduced if the MacBook Pro is always plugged into a monitor?

No.