Lysosomes—that is, acidic organelles known for degradation/recycling—move through the cytoplasm alternating between bursts of active transport and short, diffusive motions or even pauses. While their mobility is essential for lysosomes’ fusogenic and non-fusogenic interactions with target organelles, their movements have not been characterized in adequate detail. Here, large-scale statistical analysis of lysosomal movement trajectories reveals that lysosome trajectories in all examined cell types—both cancer and noncancerous ones—are superdiffusive and characterized by heavy-tailed distributions of run and flight lengths. Consideration of Akaike weights for various potential models (lognormal, power law, truncated power law, stretched exponential, and exponential) indicates that the experimental data are best described by the lognormal distribution, which, in turn, can be related to one of the space-search strategies particularly effective when “thorough” search needs to balance search for rare target(s) (organelles). In addition, automated, wavelet-based analysis allows for co-tracking the motions of lysosomes and the cargos they carry—particularly the nanoparticle aggregates known to cause selective lysosome disruption in cancerous cells. The methods we describe here could help study nanoparticle assemblies, viruses, and other objects transported inside various vesicle types, as well as coordinated movements of organelles/particles in the cytoplasm. Custom-written code that includes integrated workflow for our analyses is made available for academic use.