I read about the lotus effect on wikipedia, but I haven't found an explanation as to why droplets collecting dirt on the surface of a leaf is helpful to the flower's survival.
Lotus benefits from hydrophobicity for that it decreases the likeliness of being infected by pathogens (found in "dirt") and increase the ability to perform photosynthesis.
According to a study by Darmanin and Guittard, the plants (not only lotus) with ultraphobicity benefits from these structure for :
these structures are able to stabilize the presence of air underwater and be submerged for several weeks
Let's talk a little about the second part : having a good access to gas is vital for plants to do photosynthesis. In an environment which is very wet (like the one the lotus lives in), it is better to be dry to maximise air/plant surface area.
Now, about the self cleaning. First, lotus lives in backwater or muddy environment In this study by W. Barthlott and C. Neinhuis, it is said that big particles can occlude stomas, the small "holes" that allows the plant to breath. Wet environment is ideal for bacterial/fungal growth and different kind of disease. Unclean water could also block light and make photosynthesis less efficient.
Again, wettability is important for the adhesion of microorganisms to leaf surfaces. In addition, on waterrepellent surfaces, spores and conidia are deprived of the water necessary for germination. Therefore, the epicuticular wax crystalloids and their physical properties may be regarded as the first line of defense against pathogens.