The 3 leptons ($e,\mu,\tau$) of QED can form bound states. The positronium $e e^+$ can have spin 0 (para positronium) or spin 1 (ortho positronium). There is also muonium $e \mu^+$, true muonium $\mu \mu^+$, and similarly other bound states with $\tau$ as constituent.
What are the parities of each of these bound states? The spins and charge conjugation properties are rather clear, so in the $J^{PC}$ notation $J$ and $C$ are straightforward, but what about $P$?