The non-symmetric properties of the TLM-matrix require the application of general Krylov subspace methods for Model Order Reduction (MOR). Application of the Arnoldi algorithm is computational expensive. Furthermore, the classical non-symmetric Lanczos algorithm requires the transpose TLM-matrix in order to form a biorthogonal basis for Krylov subspaces; hence, its algorithmic simplicity is also penalized in comparison to the time-domain TLM scheme. In this paper we describe a novel scattering-symmetric Lanczos algorithm, which is faster and consumes less memory in comparison to the conventional non-symmetric Lanczos algorithm, since the S-symmetric Lanczos algorithm generates the biorthogonal basis utilizing a single sequence like the symmetric Lanczos procedure. Along with the details of the proposed S-symmetric Lanczos algorithm, estimates are provided for its computational cost in comparison to the standard implicit TLM time evolution scheme, the general Arnoldi process and the non-symmetric Lanczos process.