I own a 2002 Disco. The owners manual says 5w40 is for all temperatures. If you live where it doesn't get above 85*F then 5w30 and if you live where it doesn't get below 0*F then 10w40.
I personally use 0w30 German Castrol in the winter and Lubro Moly 0w40 in the summer.
Lots of guys with Discos run heavier oil like 20w50 dino or 15w40 HDEO dino, both with good results.
Remember the 4.0L is an ancient design engine and it seems to like oil kinda on the heavy side. For years Land Rover dealers put 20w50 in as there change oil.
The thing to be careful of on these engines isn't necessarily oil, it is sticking exhaust valves. The dealer sells a fuel treatment that is supposted to eliminate this problem. They install it at every service on vehicles brought to them. I buy a couple bottles when I go by the dealer and put it in the tank about every 5,000 miles; cheap insurance on the engine. No doubt you'll soon be out of warranty if you aren't already, and these are not cheap engines to replace.
Also, if it hasn't been done already, drop the transmission pan and change the filter. It should have been done at 30,000 miles and then never again. I usually drain the trans fluid once a year and replace it, but only because I routinely pull a 3,000 pound trailer and fresh fluid is better for that.
Good luck with the Disco, not too many Disco folks around these parts. Chris