Numerical simulations are performed for a sudden stratosphere warming (SSW) under different atmospheric tide and planetary wave forcing conditions to investigate the tidal variability in the mesosphere and lower thermosphere (MLT). The influence of variability of different tides in the MLT on generating perturbations to the low latitude ionosphere is also investigated. Significant changes are found to occur in the migrating semidiurnal solar (SW2) and lunar (M2) tides as well as in the westward propagating nonmigrating semidiurnal tide with zonal wave number 1 (SW1). The changes in the zonal mean atmosphere that occur during SSWs lead to an enhancement in the SW2 and M2 tides. The vertical wavelength of the SW2 is also changed, resulting in phase variability in the SW2 at a constant altitude. Significant enhancements in the SW1 are found to occur only in the presence of additional planetary wave forcing, and this demonstrates that nonlinear planetary wave‒tide interactions lead to the enhanced SW1 during SSWs. The amplitude and phase variability of the SW2 is found to be capable of producing temporal variability in the vertical plasma drift velocity that is similar to the observed variability. Changes in the M2 during SSWs can contribute up to an additional ∼30% of the total ionosphere variability; however, the overall influence of the lunar tide is found to be dependent upon the phase of the moon relative to the timing of the SSW. Although the influence is relatively minor, the SW1 also contributes to the low latitude ionosphere variability during SSWs. The simulation results for the vertical plasma drift velocity and total electron content (TEC) further illustrate that significant longitude variability occurs in the ionosphere response to SSWs. Key Points SW2, SW1, and M2 tides all contribute to ionosphere response to SSWs. Lunar tide contributes ~30% of ionosphere response to SSWs. Ionosphere response to SSW exhibits significant longitude dependence.