In liquid desiccant air-conditioning (LDAC) systems, the same moisture removal amount can be realized by different temperature combinations of cooling and heating sources. However, only limited studies have addressed optimal cooling and heating source temperatures for LDAC systems. In this study, analytical solutions for the optimal cooling and heating source temperatures in LDAC systems are determined under ideal conditions. Under the optimal temperatures, the minimum exergy inputs of the cooling and heating sources are achieved. The accuracy of the analytical solutions is validated based on results obtained from an enumeration method. Two critical conclusions are drawn: (i) for any solution flow rate, there is a set of optimal cooling and heating source temperatures and a minimum exergy input, whereas among different solution flow rates, there is an optimal solution flow rate leading to the minimum exergy input (calculated in this study); and (ii) once the product of the solution mass flow rate and solution specific heat capacity is fixed, the optimal cooling and heating temperatures, states of air and solutions can be uniquely determined, free from the influence of the desiccant solution type. Thus, this study provides a fundamental reference for achieving the best exergy performance in LDAC systems.