We probed the evolution of the superconducting transition temperature Tc and the normal state parameters of LuxZr1−xB12 solid solutions employing resistivity, heat capacity and magnetization measurements. In these studies of high-quality single crystals it was found that there are two types of samples with different magnetic characteristics. An unusually strong suppression of superconductivity in LuxZr1−xB12 with a rate dTc/ dx = 0.21 K/at.% of Lu was observed previously on the first "magnetic" set of crystals, and it was argued to be caused by the emergence of static spin polarization in the vicinity of non-magnetic lutetium ions. On the contrary, the second (current) set of "nonmagnetic" crystals demonstrates a conventional Tc(x) dependence with a rate dTc/ dx = 0.12 K/at.% of Lu which is typical for BCS-type superconductors doped by nonmagnetic impurities. The reason for this difference is yet unclear. Moreover, the H−T phase diagram of the superconducting state of LuxZr1−xB12 (0 ≤ x ≤ 1) solid solutions has been deduced from magnetization measurements.