I did this for my Discovery 3 a couple years back and I figured I would share some pics and details.
I don't know how the rest of you feel about the nameplate "LR3" but I think it's F'ing stupid and redundant. What is it? A Land Rover Land Rover 3? It's especially frustrating when you factor in the Freelander 2's LR2 badge and the LR4. It's all nonsense. Some idiot at LR came up with this nomenclature with the misguided idea that Americans love X5s, G500s, LX470s, etc simply because of their alphanumeric models. Luckily they have already stated the Discovery name will return on the next model!
Anyway, here are the part numbers:
"DISCOVERY" part # DAH500020LPO
"3" part # DAB500160LPO
Easily sourced from ebay.co.uk
Remember to mark the Bottom and Left edges of your current badges with masking tape before you remove them to get the alignment correct. Use fishing line to easily remove the old "LR3" and throw that S#it out.