You could in theory, but you can't mix and match remotes from different locksets.
It also screws up the lockset that belongs to the vehicle - meaning if you did acquire a new remote fob from LR for your vehicle, it then wouldn't work (in the same way that if someone changed the BECM and lockset etc, you'd be out of luck too). Our red P38 is an example of this - mostly my own doing. The pair of physical key blades and various locks/barrel are from my first old P38, and the pair of remote fobs are from another scrapped P38, as the original remote fob we got with the vehicle had failed. So its a total mess and if we ever sold it and the new owner wanted another key, they're going to have real issues.
Won't have any battery drain issues though with its prototype fob filter still in place and working ;)
Last I heard however, LR were still supplying new remote keys for UK vehicles, but possibly not for NAS vehicles now.
On top of that, the BECM needs unlocking to make this possible - Marty has the kit to do that. He kindly unlocked both my test bench and red P38's BECMs so that we could develop the receiver fob filters with various remote fobs. Coincidentally my P38's BECM is also unlocked, but it was also a vehicle owned by LR for the first two years of its life - so I have no idea of the history or reasoning behind it. Handy though!
New aftermarket keys are available from a couple of sources, and we're in the process of developing our own remote fob too. We have prototypes that work and have proven the concept just fine - but with my house refurbishment, actual work and generally life in the way, progress hasn't moved on much further yet.
Might well be by the summer we have them available - with a couple of options too for the type of key/remote. Cheap too. The complicated bit will be how we get your fob code of your existing key if you have a working one. If you have no working remote, we'd need to get hands-on with the BECM etc.