pressure washing it at our water park almost every day
Is there any corrosion on the screws and springs? If the metal parts aren't dried after exposure to water, they can rust, which decreases the turning quality.
As for lubricant, you want use one which is silicone-based. Petroleum-based oils can soften or weaken the plastic over time, and vegetable-based oils can go gummy and rancid.
My go-to is to disassemble the puzzle, wipe off any plastic dust and lubricant residue, and wash the plastic pieces in warm soapy water. Once the pieces are thoroughly rinsed and dried, I reassemble the puzzle, judiciously applying silicone oil to key contact surfaces.
Do you know the brand and model of your cube?