do you still pay blue Diana's ability on resolution?

Yes — Diana, Lunari's [1] is paid on resolution, not when the trigger hits the Chain.

The "you may pay [1]" is an instruction inside the triggered ability, so it's evaluated when the ability resolves (Rule 444.3, 404.2). You choose at that moment whether to pay; if you decline, the whole effect is ignored (Rule 444.2). Even if Diana is recalled/killed in response, the ability is already on the Chain and resolves independently of its source — so you can still pay the [1] and Predict/reveal.