Optical cooling techniques of solid-state refrigerators, especially those toward the cryogenic temperature range, have attracted considerable attention in the fields of space exploration, precise measurement, material sciences, and so forth. Here, we report the laser cooling of the 7.5% Yb3+-doped LuLiF4 crystal down to 121 K reaching NIST's designated range of cryogenic temperatures (<123 K). Further results based on the cooling window indicate a promising cooling limit of 59 K, provided with enhancement in pump absorbance and heat load management of the sample. Our work, therefore, can motivate an all-solid-state optical refrigeration application beyond the liquid nitrogen boiling point, thus bringing great opportunity to realize cryogenic coolers and radiation-balanced lasers in miniaturized systems.