ssddx :
i have no experience with lucidsound. it seems hard to find any "credible" well done reviews or comparisons. those that i do find are just comparing the ls20 to ls40. from the little i did read on lucidsound it seems that they at least were not terrible though competing with the a50 and similar better headsets in that budget range for quality and comfort. not bottom rung but certainly not perfect either.
the game one is based on the hd518/hd558 so will be fairly neutral with perhaps just a hint more bass. it has a more well known signature that you can compare with other well known headsets fairly easily. it is easier to know if it will work for you or not.
headphone setup is a little more complicated with the ps4 over usb headsets but there are devices to give you virtual surround if you cared for it. virtual is not strictly required (its a love or hate it scenario) and technically it distorts the audio quality to get the effect. some purists are perfectly happy with stereo while some people cannot seem to live without virtual. pick your poison.
whether you wanted to invest in equipment to get headphones to work with ps4 well depends on your preferences for audio honestly. if you would rather have something "nice" sounding or just want something "good enough" but easy to hook up.
if you end up going that route, there are other headphones open to use and the modmic can turn any of them into a headset.
since you specify immersion over competitive audio it sounds like a "v-shaped" signature might fit you. these emphasize explosions and vocals so often give that "fun" sound to audio. the dt990 (or dt770 if you want closed) do this well. fairly neutral with just a hint of bass could also be up your ally. the dt880, hd518/558/598 and some akg cans do this well.
TLDR:
it comes down to if you want the convenience of usb hook up without additonal devices or if you want to focus on sound quality over convenience. also, if you care about virtual surround would influence if/what you would need for a non usb set.
Thank you for the long reply.
See, i thought I would prefer neutral sound over v-shaped signature because isn't neutral supposed to have more clarity whereas v-shaped drowns out clarity with bass and treble?
I don't really want to buy any further equipment like a Mixamp or anything to improve the sound. The less clutter the better. Can the Game One be used to full effect through the PS4 controller?
I guess i don't really have a preference for either Virtual surround sound or stereo. So i guess my main question is if the wider frequency response of the Game One is better than having DTS headphone X from the LS40?
The game One having a frequency response of 15-28,000hz whereas the LS40 has the standard 20 - 20,000hz.