For cholesteric liquid crystals (CLC) based on azoxy nematic ZhK-440 and cholesterol esters, variation of selective reflection band maximum with temperature and under irradiation by light of different wavelengths were studied. In these materials, lasing is hindered because fluorescence quantum yield of most lasing dyes falls sharply at concentrations 0.3-0.5wt.%. We have shown that for some phenolenone and pyrromethene dyes the fluorescence quantum yield in such systems reaches 50% and more. Lasing has been obtained in CLC on the basis of azoxy nematic ZhK-440, with reversible phototuning by 30nm towards shorter, and by 20nm - towards longer wavelengths.