Optical cooling of solids, relying on annihilation of lattice phonons via anti-Stokes fluorescence, is an emerging technology that is rapidly advancing. The development of high-quality Yb-doped fluoride single crystals definitely led to cryogenic and sub-100-K operations, and the potential for further improvements has not been exhausted by far. Among fluorides, so far the best results have been achieved with Yb-doped (YLF) single crystals, with a record cooling to 91 K of a stand-alone YLF:10%Yb. We report on preliminary investigation of optical cooling of an (LLF) single crystal, an isomorph of YLF where yttrium is replaced by lutetium. Different samples of 5% Yb-doped LLF single crystals have been grown and optically characterized. Optical cooling was observed by exciting the Yb transition in single-pass at 1025 nm and the cooling efficiency curve has been measured detecting the heating/cooling temperature change as a function of pumping laser frequency.