Abstract The radius valley, a dip in the radius distribution of exoplanets at ∼1.9 R ⊕, separates compact rocky super-Earths and sub-Neptunes with lower density. Various hypotheses have been put forward to explain the radius valley. Characterizing the radius valley morphology and its correlation to stellar properties will provide crucial observation constraints on its origin mechanism and deepen the understanding of planet formation and evolution. In this paper, the third part of the Planets Across Space and Time series, using the LAMOST-Gaia-Kepler catalog, we perform a systematical investigation into how the radius valley morphology varies in the Galactic context, i.e., thin/thick galactic disks, stellar age, and metallicity abundance ([Fe/H] and [α/Fe]). We find the following: (1) The valley becomes more prominent with the increase of both age and [Fe/H]. (2) The number ratio of super-Earths to sub-Neptunes monotonically increases with age but decreases with [Fe/H] and [α/Fe]. (3) The average radius of planets above the valley (2.1–6 R ⊕) decreases with age but increases with [Fe/H]. (4) In contrast, the average radius of planets below the valley (R < 1.7 R ⊕) is broadly independent of age and metallicity. Our results demonstrate that the valley morphology, as well as the whole planetary radius distribution, evolves on a long timescale of gigayears, and metallicities (not only Fe but also other metal elements, e.g., Mg, Si, Ca, Ti) play important roles in planet formation and in the long-term planetary evolution.