Why would you need Audeze to make a dac/amp to try the LCD-GX?
The LCD GX can be driven just fine for through the jack on the controller (really not bad at all).
If you want a dedicated dac, you can use something like the schitt hel 2.
I use the LCD GX as my daily headphone for gaming and on PS5 I hook it up through the Astro Mixamp Pro TR
https://www.astrogaming.com/en-gb/products/mixamps/mixamp-tr-gen-4.html
I wouldn't recommend that over the Schit Hel 2 based on what I've read, but it's what I already had and it has it's own 5.1 virtual surround implementation via Dolby which was especially valuable on PS4 and PS3 where there was no system-level virtualisation.
On the XBOX and Switch, I just plug it directly into the console/controller itself. On my PC I either use the mixamp, my zen dac, or just by plugging it directly into my PC via the mic/audio splitter.
Like I say, the LCD GX is my daily driver for both games and music and I love it. It always sounds great whatever I throw at it which is what makes it perfect for me because I have such a diverse array of devices and applications where I want to use it.