We present a detailed analysis of the vertical and radial structure of mono-age stellar populations in three edge-on lenticular galaxies (FCC 153, FCC 170, and FCC 177) in the Fornax cluster, using deep MUSE observations. By measuring the half-mass radius (R$_{50}$) and half-mass height (z$_{50}$) across 1 Gyr-wide age bins, we trace the spatial evolution of stellar populations over cosmic time. All galaxies exhibit a remarkably constant disc thickness for all stars younger than ~6 Gyr, suggesting minimal secular heating and limited impact from environmental processes such as tidal shocking or harassment. Evidence of past mergers (8-10 Gyr ago) is found in the increase of z$_{50}$ for older populations. We find that accreted (metal-poor) stars have been deposited in quite thick configurations, but that the interactions only moderately thickened pre-existing stars in the galaxies, and only caused mild flaring in the outer regions of the discs. The radial structure of the discs varies across galaxies, but in all cases we find that the radial extent of mono-age populations remains constant or grows over the past 8 Gyr. This leads us to argue that within the radial range we consider, strangulation, rather than ram-pressure stripping, is the dominant quenching mechanism in those galaxies. Our results highlight the usefulness of analysing the structure of mono-age population to uncover the mechanisms driving galaxy evolution, and we anticipate broader insights from the GECKOS survey, studying 36 nearby edge-on disc galaxies.