In absorption systems using the aqueous lithium bromide mixture, the Coefficient of Performance is affected by the desorber. The main function of this component is to separate the refrigerant fluid from the working mixture. In conventional boiling desorbers, constant heat flux and vacuum pressure conditions are necessary to carry out the desorption process, and usually, the absorbers are heavy and bulky; thus, they are not suitable in compact systems. In this study, a membrane desorber was evaluated, operating at atmospheric pressure conditions with a water/lithium bromide solution with a concentration of 49.6% w/w. The effects of the solution temperature, solution mass flow, and condensation temperature on the desorption rate were analyzed. The maximum desorption rate value was 6.1 kg/m2h with the following operation conditions: the solution temperature at 95.2 °C, the solution mass flow at 4.00 × 10−2 kg/s, and the cooling water temperature at 30.1 °C. On the other hand, the minimum value was 1.1 kg/m2h with the solution temperature at 80.2 °C, the solution mass flow at 2.50 × 10−2 kg/s, and the cooling water temperature at 45.1 °C. The thermal energy efficiency, defined as the ratio between the thermal energy used to evaporate the refrigerant fluid with respect to the total thermal energy entering the membrane desorber, varied from 0.08 to 0.30. According to the results, a high solution mass flow, a high solution temperature, and a low condensation temperature lead to an increase in the desorption rate; however, a low solution mass flow enhanced the thermal energy efficiency. The proposed membrane desorber could replace a conventional boiling desorber, especially in absorption cooling systems that operate at high condensation temperatures as in warm weather regions.