We report a strategy of using vapor transport chemical vapor deposition (CVD) to prepare well-faceted, high crystal quality organic-based lead halide perovskite platelets on muscovite mica substrates. The well-defined single crystal nanoplatelets of lead halides were first grown on mica substrate utilizing van der Waals epitaxial growth following by thermally intercalating of methyl amino halide (gas phase) into pre-grown lead halide platelets. The resulted CH3NH3PbI3 platelets showed an electron diffusion length of more than 200 nm which is approximately two times higher than that of the solution processed film. This synthesis approach will create a new platform to exploit the physical properties of the organic-based lead halide perovskites. The as-grown platelet crystals exhibit excellent optical properties, as studied by optical absorption and photoluminescence spectroscopy. Notably, we demonstrate an optically pumped room-temperature near infrared laser based on the CH3NH3PbIaX3-a (X= I, Br, Cl) nanoplatelets. Their large exciton binding energies, long diffusion lengths and naturally formed high-quality planar whispering-gallery mode cavities ensure adequate gain and efficient optical feedback for low-threshold in-plane lasing. The whispering-gallery type planar perovskite nanolasers have pronounced optical gain and tunable optical modes, which can be potentially expanded with controllable emission from UV to NIR. Our research opens alternative routes beyond III-V nanostructures in achieving near infrared solid state nanolasing and will inspire more designs of low-threshold near-infrared nanolasers pumped optically and electrically.