What's the relationship between a custom recovery and rooting? So I want to make sure I understand everything. 

If I want a Recovery, I need to root my phone. I have an LG G2. Clockwork is a recovery; If I download ClockworkMod recovery and use Flashify without rooting my phone, will that eventually root my phone through ClockworkMod flashing? Or should I root my phone with ioroot.zip first, and then flash a recovery?
You don't need to root your phone in order to use a custom recovery like TWRP or ClockWorkMod.

It will only root your phone if you use it to...


flash a rooted image
flash a su binary
restore a rooted backup


It is common for recoveries to offer to root when you restart, but you can just say "No" if you don't want to root.