To temporarily disable the lights, run the following two commands:
echo none | sudo tee /sys/class/leds/led0/trigger echo 1 | sudo tee /sys/class/leds/led0/brightness
To permanently disable the lights, edit the boot config file using the following command:
sudo nano /boot/config.txt
Once in the file, add the following lines to the bottom:
# Disable the ACT LED on the Pi Zero dtparam=act_led_trigger=none dtparam=act_led_activelow=on
Exit the nano text editor using Ctrl+X and enter Y to save. Then reboot the Pi using the following command.
I got this code from here, but the formatting on the website was a little messed up so I reposted here.
Picture is from diyprojects.io.