When the range is approaching 0, I fill up. I complained about this before - the range calculation is overly conservative, and for quite a while when I first purchased the car I was convinced the fuel tank of the LR4 was smaller than advertised, 20-21 gallons tops (coming out of my 2006 Sport where I had the opposite problem... I ran out of gas a couple of times by trusting that stupid computer.)
It's not an exact science on the LR4, either. With 5-10 miles or less of range left, I have filled up with as little as 18 gallons or as much as 21. That's quite a swing, and it's got everything to do with the estimates the computer makes based on your most recent mileage and driving conditions. If you are stuck in stop-n-go traffic for an hour and the range shows 10 miles left, chances are you really don't have too much fuel left at that slow pace, and you'd be pushing your luck by going too far past the 0 range. If you are coasting down the highway, you may have enough fuel to drive another 50-60 miles before you are actually on fumes.
We all know it's not a good idea to let the tank run dry or near-dry anyway and suck potential fuel deposits into the engine. So, I fill up when the car tells me I should even though I am fairly sure I still have several gallons of gas left and could probably make it home and back without a problem. I do wish the tank was larger. The new Sport has a 27.5-gal tank AND gets better mileage thanks to the lower weight and the SCV6 engine, so you can reasonably expect 450-500 miles with a tankful of gas. I am lucky to get 300-350 miles out of my LR4. Besides the depressing frequent stops at the gas station, that can be an issue when overlanding.