The structural, elastic, elastic anisotropic, thermodynamic and electronic properties of Lonsdaleite C, Si and Ge and Lonsdaleite C-Si and Si-Ge alloys are investigated using density functional theory. The elastic anisotropy calculations show that the Lonsdaleite C0.25Si0.75 alloy has the greatest anisotropy in Poisson's ratio, shear modulus, bulk modulus and Young's modulus. Through the mixing of carbon and silicon and silicon and germanium at certain proportions, Lonsdaleite C0.25Si0.75 with metallic properties and Lonsdaleite Si0.25Ge0.75 with a direct band gap are obtained, where Lonsdaleite Si0.25Ge0.75 is a narrow direct band gap semiconductor with a band gap of 0.76 eV at the HSE06 hybrid functional level. The minimum thermal conductivity calculations on Lonsdaleite C-Si and Si-Ge alloys show that the minimum thermal conductivities of Lonsdaleite C0.75Si0.25 and Lonsdaleite C0.5Si0.5 are greater than that of diamond C, and the minimum thermal conductivities of Lonsdaleite C-Si and Si-Ge alloys in different directions are also investigated.