Priest of Titania does not have summoning sickness.
There are at least four Elves on the battlefield.
Steps
Activate
Priest of Titania by tapping it, adding ({G} magic symbol) for each Elf on the battlefield.
Activate
Wirewood Lodge's second ability by paying ({G} magic symbol) and tapping it, targeting
Priest of Titania.
Rings of Brighthearth triggers, causing you to pay ({2} magic symbol) to copy
Wirewood Lodge's ability, targeting
Priest of Titania.
Resolve the first
Wirewood Lodge ability, untapping
Priest of Titania.
Activate
Priest of Titania by tapping it, adding ({G} magic symbol) for each Elf on the battlefield.
Resolve the second
Wirewood Lodge ability, untapping
Priest of Titania.
Activate
Deserted Temple's second ability by paying ({1} magic symbol) and tapping it, targeting itself.
Rings of Brighthearth triggers, causing you to pay ({2} magic symbol) to copy
Deserted Temple's ability, targeting
Wirewood Lodge.
Resolve both
Deserted Temple abilities, untapping it and
Wirewood Lodge.
Repeat.
Once you have infinite green mana, you may repeat steps 7 through 9 targeting any other land you control instead, or repeat the combo targeting any Elves you control.