Are there natural processes we've discovered which lead to laser light of some distinct wavelength?
Yes there are. All you really need is for energy to be injected into a system, and for the particles to linger for relatively long periods of time in some excited state. For example, if you have states $A$, $B$, and $C$ in order of increasing energy, natural pumping might work well for $A \to C$ and poorly for $B \to C$. Suppose $C \to B$ occurs rapidly via spontaneous emission, but $B \to A$ takes a long time. You will end up with lots of state $B$ lying around, ripe for stimulated emission.
In particular, we see masers in all sorts of environments in space, including around active galactic nuclei powered by supermassive black holes and in star-forming regions. These tend to be microwave transitions between rotational/vibrational states in small molecules. Astrophysical sources are good places to look for natural population inversions, as explained well by that second link:
At low densities, being out of thermal equilibrium is more easily achieved because thermal equilibrium is maintained by collisions, meaning population inversion can occur. Long path lengths provide photons traveling through the medium many opportunities to stimulate emission, and produce amplification of a background source of radiation.