Having been in the automotive (sales and repair sides) 20 years ago and investments for about 5-7 years I fully endorse JWEST's recommendation of self insuring. Either way there's a gamble. As he pointed out, buying the extended warranty, which is an insurance policy, is pricey at the age of most LR3s now and is a bet that you're going to spend a lot more in repair costs than the price of the policy. Future dollars always cost more than today's dollars (unless you have massive deflation, but that's another discussion) and as JWEST pointed out you have the potential for a bit of return on your investment with a higher interest rate.
Either way, if you can lay down a chunk now, regularly deposit into that account to build it up, you will have a very nice repair reserve without any deductible, hassle, and with the option to use for something else if needed.
This is my most likely course of action once my current Ford Premium Care Extended Warranty plan expires in 2016. I'll be over 100k miles on an 8 year old vehicle, pushing towards 10 years old. In the meantime, I'm making every effort with my independent LR shop to push through every possible warranty covered repair. Additionally, Ford doesn't offer this warranty on LRs.