Chemical vapor deposition (CVD) allows lateral edge epitaxy of transition metal dichalcogenide heterostructures with potential applications in optoelectronics. Critical for carrier and exciton transport is the quality of the two materials that constitute the monolayer and the nature of the lateral heterojunction. Important details of the optical properties were inaccessible in as-grown heterostructure samples due to large inhomogeneous broadening of the optical transitions. Here we perform optical spectroscopy at T = 4 K and also at 300 K to access the optical transitions in CVD grown MoSe2-WSe2 lateral heterostructures that are transferred from the growth-substrate and are encapsulated in hBN. Photoluminescence (PL), reflectance contrast and Raman spectroscopy reveal considerably narrowed optical transition linewidth similar to high quality exfoliated monolayers. In high-resolution transmission electron microscopy (HRTEM) we find near-atomically sharp junctions with a typical extent of 3nm for the covalently bonded MoSe2-WSe2. In PL imaging experiments we find effective excitonic diffusion length that are longer for WSe2 than for MoSe2 at low T=4 K, whereas at 300 K this trend is reversed.