Magnetic susceptibility and electron spin resonance experiments in the rare earth (R = Nd, Er, and Yb) 5-25% doped cubic intermetallic LuInNi4 enable estimates of the fourth A4 and sixth A6 order crystal-field parameters for this compound. These parameters yield a Γ6 doublet, a Γ7 doublet, and a Γ8 quartet as the ground states for Nd3+, Er3+, and Yb3+, respectively, and an overall crystal-field splitting of 100-300 K. The A4 and A6 parameters are found to have comparable order of magnitude for all the R studied and their values are in agreement with reported values for other cubic systems.