The Leishmania lysosome has an atypical structure, consisting of an elongated vesicle-filled tubule running along the anterior-posterior axis of the cell, which is termed the multivesicular tubule (MVT) lysosome. Alongside, the MVT lysosome is one or more microtubules, the lysosomal microtubule(s). Previous work indicated there were cell cycle-related changes in MVT lysosome organization; however, these only provided snapshots and did not connect the changes in the lysosomal microtubule(s) or lysosomal function. Using mNeonGreen tagged cysteine peptidase A and SPEF1 as markers of the MVT lysosome and lysosomal microtubule(s), we examined the dynamics of these structures through the cell cycle. Both the MVT lysosome and lysosomal microtubule(s) elongated at the beginning of the cell cycle before plateauing and then disassembling in late G before cytokinesis. Moreover, the endocytic rate in cells where the MVT lysosome and lysosomal microtubule(s) had disassembled was extremely low. The dynamic nature of the MVT lysosome and lysosomal microtubule(s) parallels that of the Trypanosoma cruzi cytostome/cytopharynx, which also has a similar membrane tubule structure with associated microtubules. As the cytostome/cytopharynx is an ancestral feature of the kinetoplastids, this suggests that the Leishmania MVT lysosome and lysosomal microtubule(s) are a reduced cytostome/cytopharynx-like feature.