Degradation of endocytosed proteins involves the formation of transient connections between late endosomes and lysosomes in a process called "kiss and run." Genes and proteins controlling this mechanism are unknown. Here, we identify the small guanosine triphosphatase (GTPase) RabX1 as an organizer of a late endosomal compartment that forms dynamic tubular connections to lysosomes. By analyzing trafficking of the adhesion protein Fasciclin2 in the Drosophila follicular epithelium, we show that a reduction of RabX1 function leads to defects in Fasciclin2 degradation. RabX1 mutants fail to form normal lysosomes and accumulate Fasciclin2 in a swelling late-endosomal compartment. RabX1 protein localizes to late endosomes, where it induces the formation of tubular connections to lysosomes. We propose that these tubules facilitate influx of lysosomal content into late endosomes and that this influx leads to the formation of endolysosomes, in which Fasciclin2 is degraded. We show that the formation of RabX1 tubules is dependent on the V-ATPase proton pump. Moreover, we provide evidence that V-ATPase activity is upregulated during epithelial differentiation. This upregulation intensifies RabX1 tubulation and thereby boosts the capacity of the endolysosomal pathway. Enhanced endolysosomal capacity is required for the removal of Fasciclin2 from the epithelium, which is part of a developmental program promoting epithelial morphogenesis.