Away from criticality, when the larger lattice is built from smaller blocks, then due to the additivity property of an extensive quantity, the central limit theorem guarantees that RX ~ N−1 thereby ensuring self-averaging.
When away from criticality, building a larger lattice from smaller blocks leads to self-averaging. This is because the central limit theorem states that the sum of random variables tends towards a normal distribution as the number of variables increases, and in this case, RX ~ N−1.