Two-dimensional (2D) semiconductors offer a convenient platform to study 2D physics, for example, to understand doping in an atomically thin semiconductor. Here, we demonstrate the fabrication and unravel the electronic properties of a lateral doped/intrinsic heterojunction in a single-layer (SL) tungsten diselenide (WSe2), a prototype semiconducting transition metal dichalcogenide (TMD), partially covered with a molecular acceptor layer, on a graphite substrate. With combined experiments and theoretical modeling, we reveal the fundamental acceptor-induced p-doping mechanism for SL-WSe2. At the 1D border between the doped and undoped SL-WSe2 regions, we observe band bending and explain it by Thomas-Fermi screening. Using atomically resolved scanning tunneling microscopy and spectroscopy, the screening length is determined to be in the few nanometer range, and we assess the carrier density of intrinsic SL-WSe2. These findings are of fundamental and technological importance for understanding and employing surface doping, for example, in designing lateral organic TMD heterostructures for future devices.