If Diana Lunari is gusted back to hand does her ability still proc?

Yes, Diana, Lunari's ability still resolves even if she is removed from the battlefield (e.g., returned to hand by "Gust") after the ability has been triggered.

According to RiftJudge FAQ #9879, here is the sequence of events:

1. Trigger: When a showdown begins at the battlefield, Diana's ability is placed on the chain.
2. Response: The opponent plays a spell (such as "Gust") to remove Diana from the battlefield.
3. Resolution: The removal spell resolves, and Diana leaves the battlefield.
4. Ability Resolution: The triggered ability remains on the chain and resolves independently of its source. When it resolves:
   • The controller is given the opportunity to pay the optional cost of [1].
   • If the cost is paid, the effect ("If you do...") executes fully, as the card text does not require Diana to be present at the time of resolution to function.

This is consistent with the general rule that triggered abilities resolve independently of their source once they are on the chain.