Unsteady land-sea breezes (LSBs) resulting from time-varying surface thermal contrasts Δθ(t) are explored in the presence of a constant synoptic pressure forcing, Mg, when the latter is oriented from sea to land (α=0°), versus land to sea (α=180°). Large eddy simulations reveal the development of four distinctive regimes depending on the joint interaction between (Mg, α) and Δθ(t) in modulating the fine-scale dynamics. Time lags, computed as the shifts that maximize correlation coefficients of the dynamics between transient and the corresponding steady state scenarios at Δθ=Δθmax, are found to be significant and to extend 2 hours longer for α=0° compared to α=180°. These diurnal dynamics result in non-equilibrium flows that behave differently over the two patches for both α’s. Turbulence is found to be out of equilibrium with the mean flow, and the mean itself is found to be out of equilibrium with the thermal forcing. The sea surface heat flux is consistently more sensitive than its land counterpart to the time-varying external forcing Δθ(t), and more so for synoptic forcing from land-to-sea (α=180°). Hence, although the land reaches equilibrium faster, the sea patch is found to exert a stronger control on the final turbulence-mean flow equilibrium response. Finally, vertical velocity profile at the shore and shore-normal velocity transects at the first grid level are shown to encode the multiscale regimes of the LSBs evolution, and can thus be used to identify these regimes using k-means clustering.