The Kepler telescope has discovered over 4,000 planets (candidates) by searching ? 200,000 stars over a wide range of distance (order of kpc) in our Galaxy. Characterizing the kinematic properties (e.g., Galactic component membership and kinematic age) of these Kepler targets (including the planet (candidate) hosts) is the first step towards studying Kepler planets in the Galactic context, which will reveal fresh insights into planet formation and evolution. In this paper, the second part of the Planets Across the Space and Time (PAST) series, by combining the data from LAMOST and Gaia and then applying the revised kinematic methods from PAST I, we present a catalog of kinematic properties(i.e., Galactic positions, velocities, and the relative membership probabilities among the thin disk, thick disk, Hercules stream, and the halo) as well as other basic stellar parameters for 35,835 Kepler stars. Further analyses of the LAMOST-Gaia-Kepler catalog demonstrate that our derived kinematic age reveals the expected stellar activity-age trend. Furthermore, we find that the fraction of thin(thick) disk stars increases (decreases) with the transiting planet multiplicity (Np = 0, 1, 2 and 3+) and the kinematic age decreases with Np, which could be a consequence of the dynamical evolution of planetary architecture with age. The LAMOST-Gaia-Kepler catalog will be useful for future studies on the correlations between the exoplanet distributions and the stellar Galactic environments as well as ages.
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