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First-principles calculations were used to estimate the anisotropic elastic and thermal properties of Ti2lnX (X = C, N) and Zr2lnX (X = C, N) M2AX phases. The crystals’ elastic properties were computed using the Voigt-Reuss-Hill approximation. Firstly, the material’s elastic anisotropy was explored, and its mechanical stability was assessed. According to the findings, Ti2lnC, Ti2lnN, Zr2lnC, and Zr2lnN are all brittle materials. Secondly, the elasticity of Ti2lnX (X = C, N) and Zr2lnX (X = C, N) M2AX phase are anisotropic, and the elasticity of Ti2lnX (X = C, N) and Zr2lnX (X = C, N) systems are different; the order of anisotropy is Ti2lnN > Ti2lnC, Zr2lnN > Zr2lnC. Finally, the elastic constants and moduli were used to determine the Debye temperature and sound velocity. Ti2lnC has the maximum Debye temperature and sound velocity, and Zr2lnN had the lowest Debye temperature and sound velocity. At the same time, Ti2lnC had the highest thermal conductivity.