Injection or optical generation of electrons and holes in graphene bilayers (GBLs) can result in the interband population inversion enabling the terahertz (THz) radiation lasing. The intraband radiative processes compete with the interband transitions. We demonstrate that remote doping enhances the indirect interband generation of photons in the proposed GBL heterostructures. Therefore, such remote doping helps to surpass the intraband (Drude) absorption, and results in large absolute values of the negative dynamic THz conductivity in a wide range of frequencies at elevated (including room) temperatures. The remotely doped GBL heterostructure THz lasers are expected to achieve higher THz gain compared with previously proposed GBL-based THz lasers. VC 2015 AIP Publishing LLC.