The eternal question, should I buy an extended warranty...

If you read automotive magazines, where Land Rovers are routinely at the bottom of reliability ratings, I guess you should run and get one, pronto. If you are going to pay big bucks for it though, make sure you get an iron-clad, exclusionary policy from a reputable company or from your Land Rover dealer directly, carefully reading the fine print before signing anything. Also, if it makes little or no difference in the premium, buy the extended warranty when your factory coverage is about to run out, not now that your car is brand new and already covered for the next few years. If it turns out to be trouble-free during the next 4 years or 50K miles, you may change your mind about extended warranties. Finally, how long do you plan on keeping your new LR4? That should be a consideration as well.
I purchased my current LR4 in early 2013, I am a high mileage driver so my factory coverage was up about 18 months later. I didn't buy an extended warranty. 3 years later, I have now close to 100K miles on my car - so my extended coverage would probably be up, even if I did buy a policy - and haven't spent a penny in repairs that an extended warranty would have honored other than a set of bushings, only brakes, oil changes and other wear and tear parts (I did rear end someone and had to redo my front end... but that's no fault of Land Rover, LOL.) I had a similar experience with my previous Land Rover, a 2006 Sport that I sold with 208K miles on the odometer. Had a few issues with that one - a few struts, an EAS compressor, front hubs, but nothing that would have justified the cost of an extended warranty. I off-road both cars regularly and they are my daily drivers as well, thus the 30-35K miles per year. I change my own oil religiously and keep up with the scheduled maintenance through a trusted indy shop, that's all. I am probably very lucky.
I don't talk about it much so as not to jinx myself, but I am the poster child for
not buying an extended warranty. When you buy one of those policies, you are betting a big chunk of money against your own car's reliability. Then, you often have to fight tooth and nails with some invisible "adjustor" and "claim specialist" across the country to get back some or all of that money you gave them, if and when something does go wrong, to figure out if the part was covered or not, to get reimbursed for a rental car, etc. I am not playing that game - I basically think most / all extended warranty companies are crooks running elaborate and legalized scams...

But that's just me. I am sure plenty of other people will have an opposite opinion or experience, and will recommend you buy a policy asap.