The LR3 doesn't have a transmission fluid dipstick. To check the fluid level, you have to get under the vehicle.
Here are the official instructions for checking the fluid level. As mentioned in the directions, the car must be idling in order for the fluid to be checked. Otherwise, fluid will accumulate in the transmission oil pan and spill out when you unscrew the filler cap.
Here are the directions for changing the transmission fluid. The instructions mention removing the transmission undershield, which is held in place by six bolts. I don't know if mine is missing, but I definitely don't have that part. The transmission pan is wedged in near some of the exhaust pipes, a cross member, and the drive shaft, which makes it difficult to get to both the filler and drain plugs.
The transmission oil recommended in the LR3 manual is Shell M1375.4, which is seems to be more of a technical spec rather than an actual product. Our ZF transmission is the 6HP26, which is not unique to Land Rover; it is also used in BMWs, Jaguars, and many other cars. However, there are claims that the transmission fluid used in the LR3 is specifically formulated for our vehicle, to achieve optimal fuel efficiency, temperature, along with perhaps a special blend of additives. In any event, after doing some internet "research", I felt that Pentosin ATF1 was a good match for the LR3 transmission, possibly being even the OEM fluid manufacturer.
The dealer fluid easily costs more that $25 a liter, and with a transmission fluid change requiring at least 4 bottles, this is the most expensive fluid change for the LR3. The internet is filled with all sorts of opinions about the ZF gearbox, with some saying not to use anything else but the dealer fluids at the risk of transmission failure. There was even a Land Rover tech on another forum saying not to DIY with the LR3 transmission fluid change, claiming how critical it is to hook up the dealer diagnostic computer to make sure the fluid is between 30 and 50 degrees Celsius, at risk of underfilling or overfilling the transmission. I feel that 30 to 50 degrees C is wide enough of a range to allow the home mechanic to do the fluid change.