Cathay Delight and Pacific Sunrise is offered on even months, while Oriental Breeze and Cloud Nine is available on odd months. You can order Cathay Delight in CX lounges if there's a tended bar, but not sure if you can order the other ones as I have never seen them on the bar menu. You can only order CX signature drinks only onboard or in a CX Lounge, so I'm quite sure you can't get it in any other oneworld lounge. That being said, if you know the formula, you could always ask a bartender to recreate the drink if they have the material.

A side note, a recent trip to HND revealed not all CX lounges with a tended bar feature Cathay Delight. Instead, HND has two Signature drinks, Sweet Haneda and the Haneda Jade.