Lateral two-dimensional (2D) transition-metal dichalcogenide (TMD) heterostructures have recently attracted wide attention as promising materials for optoelectronic nanodevices. Due to the nanoscale width of lateral heterojunctions, the study of their optical properties is challenging and requires using subwavelength optical characterization techniques. We investigated the photoresponse of a lateral 2D WSe2/MoSe2 heterostructure using tip-enhanced photoluminescence (TEPL) with nanoscale spatial resolution and with picoscale tip-sample distance dependence. We demonstrate the observation of quantum plasmonic effects in 2D heterostructures on a nonmetallic substrate, and we report the nano-optical measurements of the lateral 2D TMD heterojunction width of ∼150 nm and the charge tunneling distance of ∼20 pm. Controlling the plasmonic tip location allows for both nano-optical imaging and plasmon-induced hot-electron injection into the heterostructure. By adjusting the tip-sample distance, we demonstrated the controllability of the hot-electron injection via the competition of two quantum plasmonic photoluminescence (PL) enhancement and quenching mechanisms. The directional charge transport in the depletion region leads to the increased hot-electron injection, enhancing the MoSe2 PL signal. The properties of the directional hot-electron injection in the quantum plasmonic regime make the lateral 2D MoSe2/WSe2 heterostructures promising for quantum nanodevices with tunable photoresponse.