We report a study of muon Knight shifts to investigate the formation of the heavy-fermion state in single crystals of (Ce1-xLax)(2)IrIn8. Two different kinds of Knight-shift anomalies (deviations from a linear relation between the Knight shift and the susceptibility) are found: (1) a high-temperature effect arising from depopulation of crystalline electric field levels with temperature, and (2) a lower-temperature anomaly arising from the onset of the heavy-fermion state below a characteristic temperature T*, in agreement with the "two-fluid" model of heavy-fermion formation. In Ce2IrIn8, we find T-c*= 20.0(6) K and T-a*= 15.2(1.2) K for applied field H parallel to c axis and H parallel to a axis, respectively. For the Ce diluted systems (Ce1-xLax)(2)IrIn8, x= 0.1, 0.25, 0.50, 0.70, and 0.90, T* decreases linearly for x <= 0.5, reaching zero near x=0.7, indicating the reduction in intersite f-spin correlations with Ce dilution. A comparison with nuclear magnetic-resonance measurements of Knight-shift anomalies in several other heavy-fermion compounds suggests that the observed small anisotropy in T* may be induced by the applied field, and that T* may be inherently isotropic, even in highly anisotropic materials.