Lobules (syn. phyllidia) are asexual reproductive structures on lichens.  They form from budding-off of the main thallus, and are characterized by being stratified in the same way as the main thallus, appearing as miniature versions of the main thallus.

Lobules (phyllidia) are a diagnostic characteristic of Peltigera phyllidiosa. Here, they are evident along stress cracks in the thallus (as indicated by the arrow), a common place to find lobules on a lichen (scale represents cm). (A. Fischer--2010)