The novel modified absorption heat pump (MAHP) with the H2O-LiBr working mixture for cogeneration applications is introduced. The MAHP can simultaneously produce electric energy and heat revaluation. The proposed system has the particularity that it can be powered by alternative thermal sources (such as solar energy, biomass, geothermal) or industrial waste heat, thus promoting the production and efficient use of clean energy. The effects of pressure ratio (RP), source or supply temperature (TGH), and the energy revaluation gradient (GTL) are analyzed. The critical parameters of the proposed system are evaluated, including thermal efficiency (ηTh), exergetic efficiency (ηEx), revaluated heat (Q˙A), as well as net power produced (˙Wnet). For the MAHP analysis, RP and TGH operating ranges were chosen at 1.1−15.0 and 100−160 °C, respectively. The results show that ηEx of 87% can be obtained, having the maximum performance in TGH of 120 °C, RP of 1.1, and GTL of 35 °C. The ηTh varies between 51% and 55%, having a maximum GTL of 45 °C. On the other hand, ˙Wnet achieves values between 260 and 582 kW, depending on the defined operating conditions.