The high-temperature modification of LuAgSn was obtained by arc-melting an equiatomic mixture of the elements followed by quenching the melt on a water-cooled copper crucible. HT-LuAgSn crystallizes with the NdPtSb-type structure, space group P63mc: a = 463.5(1), c = 723.2(1) pm, wR2 = 0.0270, 151 F2, and 11 variables. The silver and tin atoms build up two-dimensional, puckered [Ag3Sn3] networks (276 pm Ag-Sn) that are charge-balanced and separated by the lutetium atoms. The Ag-Sn distances between the [Ag3Sn3] layers of 294 pm are much longer. Single crystals of isotypic DyAgSn (a = 468.3(1), c = 734.4(1) pm, wR2 = 0.0343, 411 F2, and 11 variables) and HoAgSn (a = 467.2(1), c = 731.7(2) pm, wR2 = 0.0318, 330 F2, and 11 variables) were obtained from arc-melted samples. Under high-pressure (up to 12.2 GPa) and high-temperature (up to 1470 K) conditions, no transitions to a ZrNiAl-related phase have been observed for DyAgSn, HoAgSn, and YbAgSn. HT-TmAgSn shows Curie-Weiss paramagnetism with μeff = 7.53(1) μB/Tm atom and θP = −15.0(5) K. No magnetic ordering was evident down to 3 K. HT-LuAgSn is a Pauli paramagnet. Room-temperature 119Sn Mössbauer spectra of HT-TmAgSn and HT-LuAgSn show singlet resonances with isomer shifts of 1.78(1) and 1.72(1) mm/s, respectively