Holographically designed aperiodic lattices (ALs) have proven to be an exciting engineering technique for achieving electrically switchable single- or multi-frequency emissions in terahertz (THz) semiconductor lasers. Here, we employ the nonlinear transfer matrix modeling method to investigate multi-wavelength nonlinear (sum- or difference-) frequency generation within an integrated THz (idler) laser cavity that also supports optical (pump and signal) waves. The laser cavity includes an aperiodic lattice, which engineers the idler photon lifetimes and effective refractive indices. The key findings are the following: (i) the nonlinear conversion efficiency reveals resonant enhancement at those idler frequencies where the photon lifetime is high; (ii) the resonant phase-matching (PM) process between the pump and idler waves has a one-to-one link with the engineered effective index dispersion; and (iii) in the absence of any other dispersion, the lowest threshold, multi-wavelength defect modes of the aperiodic lattice laser have degenerate phase-matched pump frequencies. This set of results will potentially have a significant impact on the wavelength multiplexing in electronically switchable THz-over-fiber communication systems [U.S. patent application 20,150,248,047A1 (3 September 2015)].