I have had to replace two half-worn sets of tires on my 1998 Subaru Legacy because one tire was ruined. To avoid damage to the car’s AWD system, the maximum acceptable difference in tire circumference is only 1/4 inch. This corresponds to a difference of 0.040 inch in tread depth. Costco may be overly cautious, but I doubt they are trying to rip you off.
If your LR has a “dumb” power distribution system (i.e. open differentials and no computer control of power distribution), I believe you could get away with mismatched tires. To be sure you aren’t doing any damage, check with an LR dealer soon.
If you have standard differentials, you can have different sized tires. Different sized tires will not damage the differential, but they can cause tracking problems, that is it may feel like the front end is out of alignment.
It would cause a problem if you lock the center differential on a solid surface. But of course when you have good traction, you don’t need to lock the differential. Even with all equal tires, locking the center differential on a dry road can cause “wind up”. It occurs on turns because the rear wheels are tracking inside the front ones. If your on a surface that slips, sand, dirt, ice etc. It doesn’t matter whether your tires match or not.
As Kendahl says, “Check with an LR dealer” (or LR-qualified repair technician) “soon” is the best answer. The owner’s manual may not mention the consequences of tire size mismatch perhaps because the consequences weren’t known at the time the book was printed. But updated service information might hold the answer. Since technicians typically are the ones doing this type of work, the freshest information source would be the service information. The CostCo technician may be able to print it out for you.