I want a full size spare rim that matches what I currently have on my 2007 LR3.

 

Check your manual; it should tell you. Looks a lot like the 7JX17's from 2006 (but in 18 instead).

 

I recognize the rims but part of me wonders it they were on a RR Sport?

What is the rim size you are looking for - 18" I presume? If so, then they would most likely not have been on a Sport then so it was an LR3 I guess.

There should be a Land Rover/Cromodora part number moulded to the inside of one of the spokes.

 

This is a link I found for four 18" wheels in the UK that look to be what you are looking for - apparently off a D3. You might be able to email them and get the LR part number for them. This proves they exist at any rate.
Land Rover Discovery 18 inch Dicovery 3 Alloys - V-Twelve.co.uk

 

18" from a LR3 2007