The gapless energy band spectra make the structures based on graphene and graphene bilayers with the population inversion created by optical or injection pumping to be promising media for the interband terahertz (THz) lasing. However, a strong intraband absorption at THz frequencies still poses a challenge for efficient THz lasing. In this paper, we show that in the pumped graphene bilayer structures, the indirect interband radiative transitions accompanied by scattering of carriers caused by disorder can provide a substantial negative contribution to the THz conductivity (together with the direct interband transitions). In the graphene bilayer structures on high-κ substrates with point charged defects, these transitions almost fully compensate the losses due to the intraband (Drude) absorption. We also demonstrate that the indirect interband contribution to the THz conductivity in a graphene bilayer with the extended defects (such as the charged impurity clusters, surface corrugation, and nanoholes) can surpass by several times the fundamental limit associated with the direct interband transitions and the Drude conductivity. These predictions can affect the strategy of the graphene-based THz laser implementation.The absence of a band gap in the atomically thin carbon structures,such as graphene and graphene bilayers, enables their applications in different terahertz (THz) and infrared devices [1][2][3][4]. One of the most challenging and promising problems is the creation of the graphenebased THz lasers [5][6][7]. These lasers are expected to operate at room temperature, particularly, in the 6-10 THz range, where the operation of III-V quantum cascade lasers is hindered by the optical phonons [8]. Recent pump-probe spectroscopy experiments confirm the possibility of the coherent radiation amplification in the optically pumped graphene [9][10][11][12][13][14][15][16], enabled by a relatively long-living interband population inversion [17]. As opposed to optically pumped graphene lasers, graphenebased injection lasers are expected to operate in the continuous mode, with the interband population inversion maintained by the electron and hole injection from the n-and p-type contacts [18]. A single pumped graphene sheet as the gain medium provides the maximum radiation amplification coefficient corresponding to the quantity 4πσ Q /c = πα = 2.3%, where σ Q = e 2 /4 is the universal optical conductivity of a single graphene layer, e is the electron charge, is the Planck constant and α ≃ 1/137 is the fine-structure constant [17]. The THz