OK. $800 we can work with easily.

Obvious choice here would be the Dell U2718Q(I think about $800 or so). You get them on special every now and then. Keep an eye out.
Note the one I refer too is the U2718Q, not the UP2718Q(which is super duper .. I think HDR or some shi.... stuff ... like that. U2718Q 4K good screen apparently.


The GT 740M on the laptop won't cut it for 4K.
You can't update it either.

I also got confused thinking that the 'HP Envy' was the desktop PC.
But it turns out that it's the laptop. So it appears you're using the HP laptop as your desktop
Then I assume you turn it into a deskptop by connecting the laptop to the LG screen, for the biggerer, better-ness of the LG screen compared to the dinky laptop screen?

Either way, laptop GPUs aren't like a desktop where you can update them. They're integrated onto the mainboard.
So, if the above situation is the case, then at this point I'd say don't bother with the new screen.

It's going to be hard to determine the exact issue with your laptop screen's colour issue, but I'm guessing that it's simply due to it being a laptop screen!