A notable advantage of homomorphic signatures is that for any function \( f \) from an admissible function family \(\mathcal {F}\) , the derived signature \(\sigma _f\) can be computed from existing signatures without accessing the secret key. This paper proposes a lattice-based linear homomorphic signature (LHS) scheme in the standard model, which is proven unforgeable under non-adaptive chosen-message attacks. The security relies on the hardness of the \(\textbf{SIS}_{q,\beta }\) problem with \(\beta =k\cdot p^2\cdot n^{1.5}\cdot \log n \cdot \omega (\log n)\) , and the scheme exhibits weak context hiding. In terms of signature vector dimensions, our scheme achieves comparable results to [21] but with key improvements: it employs unitary cryptographic scheme (not multiple subsystems) and uses a single signature vector rather than multiple vectors. As a result, the practical signature size of our scheme is roughly half that of [21].