Could one wheel bigger have worn out lsd?

my lsd has recently quit working properly, it is a clutch type. it only gives significant power to the one wheel, regardless of the traction the other wheel has. this car has 2 different tires on the rear axle, one being slightly bigger than the other. the side with the bigger wheel is the side that has worn out. could the bigger tire have worn out the clutches driving that wheel? since the wheel is bigger, i ume that, to the lsd, it would be like driving in a constant circle, since the one wheel would turn slower. in a turn with an lsd, isn't it the slower wheel that is allowed to slip? what is your opinion on this?