Non-radiative (phonon scattering) lifetimes are calculated for asymmetric quantum well structures in the AlGaAs/GaAs materials system. Structures are designed in a three-level optically pumped laser configuration, and tuned for emission in the terahertz frequency range. For emission frequencies below 8.7 THz, the energy gap of the lasing levels is less than the LO phonon energy in GaAs, which leads to suppression of LO phonon scattering and consequent reduction in the competing (non-radiative) transition rate. However, suppression of LO phonon scattering is weakened by thermal broadening of the electron energy distribution, which limits radiative efficiency and the range of structures in which population inversion may be achieved. For 77 K operation, only devices with a terahertz photon energy of less than 22 meV (5.3 THz) are predicted to exhibit population inversion.