In this work, we investigate the impact of tidal torques and mass transfer on the population of double white dwarfs (DWDs) that will be observed with LISA. Starting from a distribution of DWDs at formation predicted by numerical simulations, we use a semi-analytical model to evolve DWDs under different hypotheses for the efficiency of tidal coupling and the birth spins of white dwarfs. We then estimate the stochastic foreground and the population of resolvable binaries for LISA in each scenario. Our predicted DWD binary distribution can differ substantially from the distribution expected if only gravitational waves (GWs) are considered. If white dwarfs spin slowly, then we predict an excess of systems around a few mHz, due to binaries that outspiral after the onset of mass transfer. This excess of systems leads to differences in the confusion noise, which are most pronounced for strong tidal coupling. In that case, we find a significantly higher number of resolvable binaries than in the GW-only scenario. If instead white dwarfs spin rapidly and tidal coupling is weak, then we find no excess around a few mHz, and the confusion noise due to DWDs is very small. In that scenario, we also predict a subpopulation of outspiralling binaries below 0.1 mHz. Using the Fisher matrix approximation, we estimate the uncertainty on the GW-frequency derivative of resolvable systems. We estimate that, even for non-accreting systems, the mismodelling error due to neglect of effects other than GWs is larger than the statistical uncertainty, and thus this neglect would lead to biased estimates for mass and distance. Our results highlight the need for flexible tools in LISA data analysis. Because our semi-analytical model hinges upon a simplistic approach to determining the stability of mass accretion it will be important to deepen our comprehension of stability in mass-transferring DWD binaries.