Will using low power mode damage my battery?

By 'battery life' do you mean length of time between charges or battery health (total useable life before replacement)?

It should allow you to use your phone for longer between charges, but it will not damage it.

No.

Use Low Power Mode to save battery life on your iPhone or iPad - Apple Support

No

it will help save your battery

but charge your phone when it gets 20-30%

dont let it drain more