Alternating-current (ac) magnetic susceptibility measurements for tris(dipicolinato) complexes with a trivalent heavy lanthanide ion, [N(C2H5)4]3[Ln(dipic)(3)] x nH2O (dipic = pyridine-2,6-dicarboxylate; Ln = Tb, Dy, Ho, Er, Tm, or Yb) are reported. While none of the six complexes showed a magnetization lag from the ac magnetic field of 10-10(3) Hz above 1.8 K, the Dy, Er, and Yb complexes with odd numbers of 4f electrons exhibited the magnetization lag in a static magnetic field. This phenomenon is explained to be caused by the elimination of a fast relaxation path, which is only effective for the Kramers doublet ground states in near zero field. At higher static fields, the remaining paths such as Orbach and/or direct processes govern the dynamics of the two-level systems comprised of spin-up and spin-down states. The non-Kramers complexes were found to have a nondegenerate ground state with large energy gaps from higher states, which is consistent with their fast magnetization relaxation.