Air conditioning using a liquid desiccant (LD) is an energy-efficient air purification and cooling system. However, high energy is required to concentrate or regenerate the LD. This study aimed to investigate the characteristics of membrane fouling in more detail and determine control strategies for LD concentrating using membrane distillation (MD). Two different LDs—lithium chloride (LiCl) and potassium formate (HCOOK)—were used. Because LDs require high concentrations by nature (i.e., 40 wt% for LiCl and 70 wt% for HCOOK), the concentration was started from half of those concentrations. This resulted in a flux decline with severe membrane fouling during the concentration using MD. Different membrane fouling mechanisms were also observed, depending on the LD type. Three different physical membrane fouling control methods, including water flushing (WF), air backwashing (AB), and membrane spacer (SP), were introduced. Results showed that WF was the most effective. Both AB and SP showed a marginal change to no cleaning; however, an initial flux with SP was about 1.5 times higher than no cleaning. Therefore, WF combined with the SP could maintain a high flux and a low fouling propensity in the treatment of a high-concentration solution using MD.