So normal use in spec is 1 quart for every 1000 miles (at least thats what Land Rover spec was while I was there). Yes it is burning the oil but thats what engines do, especially once they get a bit worn. One thing easy to check(not common on 4.4 and 4.2) is to make sure the pcv is not blown out(lean short term fuel trim and high idle) anything else will be consumed through rings or valve guides and if it is not smoking just keep driving it. You may want to check the plugs just to see if it is isolated to one cylinder. As for thicker oil unless it is supercharged go to 10w40 NON synthetic. (synthetic oils will be consumed easier in an engine) Also no harm in running Lucas oil treatment align with the oil change. Change your oil more frequently as older oil(over 4-5000miles) will burn faster too. This recommendation is for 2006-2009 4.4 engines. 5.0 is a totally different animal.
As for leaking oil comment. For everyone, Imagine how much oil you cook with (tablespoons usually) now imagine pouring 1 quart or litre of oil on the ground. It would be a pool the size of a car. Unless there is a large puddle of oil under a car it is not leaking a quart in 1000 miles let alone 2 litres in 4000.
There is a possibility that the seals are leaking while the engine is running, or at speed. This will not show up unless you visually check everything under the vehicle. First, check the PCV. If it is not working correctly, excessive crankcase pressure can cause leaks while underway. This will likely not show up unless the oil pressure is elevated, such as over 2000rpm. If the issue is appearing due to oil pressure issues, it is possible that the thicker oil may aggravate the issue due to higher pressures. Something else to consider here is that, if the valve seals or rings are the problem, the oil in the exhaust could easily be burned off by the catalytic convertor.