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First, LRR is a relative term. It means "better rolling resistance than tires with the same traction and wear characteristics." It does NOT mean low rolling resistance by itself.
There is a 3 way technological triangle involving treadwear, traction, and rolling resistance. In order to get great values in one area, one or both of the other areas has to be sacrificed. Car manufacturers take advantage of this by specifying low RR values and they can get away with that because they don't provide a warranty for the tires. That's why lots of folks claim the OE tires are cheap - they generally wear fast because they have low RR.
So if you are replacing OE tires, you should expect a loss in fuel economy unless you are replacing the tires with the same make and model as original.
Even if you are replacing non-OE tires, you should expect some loss in fuel economy, because worn tires getting better RR than full tread tires. New tires will get better RR as they wear, but when you replace them, the same thing will happen.
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