The design problem of the fixed-lag smoothing and filtering in linear discrete-time stochastic systems is considered. Using the idea of invariant imbedding method [\textit{S. Nakamori}, Signal Process. 58, 309--317 (1997; Zbl 1005.94516)], new recursive least-squares fixed-lag smoothing and filtering equations are derived, where the information of factorized autocovariance function of the signal and the variance of the observation noise play important roles in estimation. The fixed-lag smoothing error variance function is derived and it is shown that the fixed-lag smoothing error is not worse than the filter. Numerical simulation results are presented for illustration.