Automatic gearbox takes a long time before it will change gears

1. Check the transmission fluid level.
2. When you draw out the dip stick to check the level, note the colour of the ATF and the smell.

follow this link to register at toyota online and down load a owners manual which will give all the spec's, quantities etc ( there free )
http://www.toyota.com/owners/web/pages/resources/owners-manuals

IMO it's more likely that you have the wrong grade of ATF. It's very important to have the correct grade. The following site shows this:
http://www.nairaland.com/1364064/automatic-gearbox-problems
each car manufacturer has recommended grades of Automatic Transmission Fluid, BMW is no exception. the following website for BMWs may bring you more accurate data:
http://www.nairaland.com/1364064/automatic-gearbox-problems
Apparently CTSC is the supplier for BMWs via the web.
Generally auto gearboxes have drain plugs and filler plugs to enable oil change in routine maintenance. But I would definately go back to the garage where you had the last service and ask politely about the grade of ATF used, before considering an 'oil change'.
Good Luck

Get a friend to depress the throttle fully. Make sure the opening value is fully open, take of air intake to view. Release the throttle. Now check that the kickdown cable is not slack. If it is loosen the outer cable nut and adjust so that the outer cable is 1mm from the stopper, that is from the rubber crommet where the cable comes through. The stopper is the big round thing.

Bit of a long shot, but check the output of the throttle position sensor with a multimeter.

Also, check that the low range switch isn't continually reporting that you are in low range. The gearbox computer adopts a VERY harsh shift pattern in low range, holding gears until approx. 3500 RPM and even then producing very hard shifts.

Try unplugging the connector that carries the low range sense signal from the transfer box under the vehicle and see if that makes a difference.

Market JapanYear 05/1999Make TOYOTAModel LAND CRUISERFrame HDJ101

Vehicle characteristics
GRADE: VXL: VXL TYPE DESTINATION: JPN: JAPAN ENGINE: 1HDFTE: 4200CC DIESEL TURBO TRANSMISSION: ATM: AUTOMATIC TRANSMISSION GEAR SHIFT TYPE: 4FC: ATM, 4-SPEED FLOOR SHIFT COLOR CODE: 057
TRIM CODE: FG41

Take it in & have it scanned, may only be a faulty solenoid or even brake switch may cause code & symptoms. Sooner you get it in, the cheaper it will probably be to repair it

and this is a 2007?
tell the dealership. you have warranty on the vehicle. they'll fix it.

U buy the biggest oil cooler u can fit in front of your radiator.