Briefly: yes, it's possible (but very unlikely); small pressurized aircraft are the more likely scenario; maybe it has happened but if so it's very rare.
According to the FAA's AC on Aircraft Operations at Altitudes
Above 25,000 Feet Mean Sea Level or Mach
Numbers Greater Than .75 it's possible and more likely to happen in a smaller pressurized aircraft:
(a) Explosive Decompression. A change in cabin pressure faster than
the lungs can decompress. Most authorities consider any decompression
that occurs in less than 0.5 seconds as explosive and potentially
dangerous. This type of decompression is more likely to occur in small
volume pressurized aircraft than in large pressurized aircraft and
often results in lung damage. [...]
Decompression. A change in cabin pressure where the lungs can
decompress faster than the cabin. The risk of lung damage is significantly lower in this decompression compared to an explosive decompression.
Unfortunately they don't cite any statistics or source for the statement "often results in lung damage" so it isn't clear when it has actually happened. Other sources suggest that it's very rare, for example Beyond the Black Box: The Forensics of Airplane Crashes says this:
The Air Force reports no serious injuries resulting from rapid
decompression with open airways, even while wearing an oxygen mask.
However, disastrous, even fatal consequences can result if the breath
is forcibly held with the lungs full of air. [...]
Lung damage is considered nearly impossible in a commercial aircraft
because of the large volume of air inside the plane. [...] Even Aloha
Flight 243 [...] did not decompress fast enough to cause internal
In other words, it's not going to happen unless you hold your breath, but another source says that you won't be able to do that anyway:
I've had pilots tell me they would be able to hold their breath [in order to extend the time of useful consciousness]. That won't happen. First of all, the surprise of
the event will override any defensive measure you may have thought you
could put into place. Secondly, the rapid change in pressure
differential will make it impossible to hold your breath. (Remember,
we can be talking about a pressure differential of 8.8 PSI. Let's put
these pressure differentials into perspective. A differential of 8.8
PSI is 1267 pounds per square foot.
I think the surprise is a key point here: the flight or fight response increases your breathing rate so even if it were physically possible to hold your breath it's extremely unlikely that you would do so.
Interestingly, Google finds numerous sources that claim lung injuries are commonly caused by aircraft decompression, but I couldn't find any source that mentioned a specific incident or even any statistics on it. I did find one book that studied 47 incidents of aircraft decompression but there was only one single barotrauma event among them and it affected the ears, not the lungs.