There are several modes to the suspension; Sleep Mode, Preliminary Mode, Post Mode, Stance Mode, Drive Mode, Speed Lowering Mode, Towing Mode, Rough Road Detection, Leveling Inhibits, Jacking Mode, Inclination Mode, phew!
When it comes to lowering the car, the most important consideration is the Speed Lowering Mode;
- When the vehicle maintains a speed of 160 km/h (100 mile/h) or above, and 10 seconds elapse, the suspension lowers 15mm below the standard ride height.
- The suspension returns to a standard ride height when the vehicle speed decreases below 140 km/h (88 mile/h) and 5 seconds elapse.
So what this means is, you need to allow for this extra 15mm of height reduction when lowering the car. OK not everyone can legally drive at >160km/h, but nevertheless it should be safe if you ever get the chance, keep this in mind.
OK lets look at the height sensors;
On the very early X350's there is a sensor at each corner, after VIN G26872 there was only the one sensor at the front, with the two at the rear, as we discovered HERE
I'm still not convinced that this is the best setup, I would like to see a sensor at each corner, but anyway that's not the point of this thread...
The front sensors look like this;

The rear sensors look like this;

They are bolted to the body of the car, and as you can see they have connecting rods, which attach to the suspension arms. As the suspension moves up/down the rods move levers, which rotate a rotary sensor.
The signals go back to the ASM, which tries to keep the front at 386mm, and the rear at 371mm (+/-15mm of course!) unless you trigger one of the other modes mentioned above.
Right so that's the background, let's have a look at the possibilities!
1. Extended/Adjustable Links on the Height Sensors
This is a popular mod on Range Rovers and Mercedes with air suspension.
The longer rods trick the sensor into thinking that the car is actually higher than it is, and so it lowers itself accordingly. Here is an example of a lowering link kit from a Range Rover Sport;

The beauty of these is they are adjustable so you can fine-tune the height at each corner (yes RR's have a sensor at each corner, cause that makes sense!)
BUT sadly, nobody makes these rods to suit the X350...I looked into making them myself but I couldn't find the pieces off-the-shelf and I don't have the time/money/patience to start up a cottage industry here...
So, until someone comes up with the product, this idea doesn't help us...
2. Shims under the mounting brackets of the height sensors
Another trick from the Mercedes crowd, usually they just put washers under the brackets, apparently a 5mm washer = 25mm drop, or something like that. It kind of works the same way as the adjustable/extended links, you are just tricking the sensor into measuring with an offset.
I looked into this as an option, being nice and cheap, however I decided against it, because;
a. I can't get under the car easily at home
b. I'm not convinced that this would work very well with only one sensor at the front
You are all welcome to try it, but I decided to pass and go for option 3..
3. Re-calibrate with a WDS, IDS or SDD diagnostic kit
The WDS, IDS or SDD as it's called these days is the dealer-level diagnostic system for Jaguar's and Land Rovers. You can't buy them at Autozone and they ain't cheap either.
I'm not going to elaborate too much more on the IDS, just how to use it to lower your car. Let's make another thread to discuss the machine itself.
It's basically, a laptop, with software and a special USB to OBDII interface;

You connect it up to the car;

And you can diagnose faults, change settings, and re-program the electronic stuff in the car. You can also calibrate the ride height.
So once you are connected up....

The car is scanned & identified, and eventually you can go into the Service Functions...

....where you have the option of Calibrating the air suspension.
You then have to follow the instructions; ignition off, on, start engine, wait, the system levels out and adjusts the suspension, you hear the compressor run and the shocks fill & bleed, eventually it levels out at what it thinks is the correct ride height.

Which is...front at 386mm, and the rear at 373mm, remember these numbers, they are important. If the car isn't sitting at this height, then it needs calibrating to the factory settings, then once it's right, you can go back in & start to lower it.

OK here is where you are meant to have the special tool to measure the ride height, looks like this;

I don't have this tool, so I had to go for the tape measure.

Not as accurate, but so long as you always measure the same way, it does work. Here's a tip, remove the center caps from your wheels, the growler (on mine at least) has a line exactly in the middle if you turn it 90°, helped a lot. Also look at the picture of the tool, it measures from the inside edge of the wheel arch, this is not the same as the outside edge!
Whatever you do, just be sure that you measure the same way each time.
Right, now the trick is, to add the amount that you want to lower the car compared to the factory ride height, to the value you enter in the IDS.

Example, if you want to lower the front by 15mm, to 371mm, and the front is actually at the factory height of 386mm, then enter 401mm into the IDS. Measure the other side and add the same amount. Maybe you don't want to lower the same amount front & rear? Then just add the amount you want to lower to the value.
After you've done all four corners, the car will go through a leveling cycle and adjust to the new height.

You then have to go and measure all four corners again.

Now here the car is thinking that it's actually at the standard factory ride height. If all's gone well, your measurements should equal factory ride height minus the lowered amount.
Once again you have to enter values into the IDS, by adding the amount you want to lower the car. Continuing the example from above, you should now be measuring 371mm, add 15mm to it & enter 386mm. The factory value!
If all goes well....

You should get a happy message!
When I first did this I dropped the front by 20mm and the rear by 10mm.
After a few days I realised that it was too low at the front, so I re-did it with a 15mm drop and it's much better now.

Still got room for the further 15mm drop on the Autobahn.
Sooo...that's that. I seriously doubt that a Jaguar Dealer would do this for you, best bet would be an independant workshop...