Walked around my 2011 Jaguar XJL today and saw that my 2 front tires and left rear tire are 245/45 and my right rear tire is 275/40 instead of 2 275/40s in the rear (car is on factory 19 inch Tobas) Are the wheels themselves staggered? I have 2 spare Tobas from the previous owner but both are 245/45. Not sure if I need to buy a rear wheel or just new tires.

 

Front wheels are 9J and rear wheels are 10J ,
if you do need to find a replacement rear the try eBay, not sure if it is possible to fit the narrower tyre on the 10” rear so you will need to remove the wheel to look at the size stamped inside, then you will know if you need to buy another rear wheel and tyre ( keep the other for a spare front ) or just buy the correct larger tyre

 

That is odd, but it is possible that someone (keeping in mind yours had only 1 previous owner I believe) replaced the right rear with a front wheel.
I believe the OD of the wheel would be the same. Without doing the math, I think the 245/45 OD comes out the same as the 275/40.
But it sure would look odd from behind the car.
The staggered fitment of the 10" on the rear and 9" on the front is an annoyance with the tires I put on it since they're directional, can only rotate side-to-side on the same axle.
I believe rear rims are easier to find than fronts though, front 9" rims are scarce for the Toba. But for the rear 10" rim, more available.

 

Asymmetrical tires not directional tires as then you could not rotate side to side only front to rear. And, I believe, only the AWD XJs can run directional.

 

Yes, I mis-typed there, the Michelins I replaced the Perellis with aren't directional (I confused them with the Perelli's before) and can be swapped side-to-side without dis-mounting.
To rotate the asymmetric Perelli P-Zero Nero's that came with it, they had to come off the rim and get flipped to swap sides.