The mountain lion chirp is also the mountain lion whistle; two names for the same vocalization. The whistle is somewhat like a chirp. There is an overlap or merging and it is difficult to describe either sound. I believe that the mountain lion whistle is more a high-pitched, cheeping, whistle. It is a difficult sound to imitate and even describe.
But I’m convinced that when people ask why mountain lions chirp they are asking the question why mountain lions whistle.
There is a video on Vimeo which can’t be embedded because of privacy settings which is said to demonstrate the mountain lion chirp. The maker says the cat is calling which is clearly happening. Having listened to it I can see the connection to the bird’s chirp but I can also see the similarity with a whistle. This is why I have said there is an overlap or a merging of the two sounds and people have called the same sound by two different names.
So why do mountain lions chirp or whistle? We’re not sure but it seems that this call which is made during crepuscular hours is made out of frustration or to serve as a form of advertisement. By advertisement I presume it is meant that the mountain lion is advertising her presence to other animals most likely other mountain lions. It is a sound which can travel quite a long way, as far as 300 m. A person who had a tame young female mountain lion said that when he called her by her name and gave her a treat she always responded with the “cheeping whistle”. In this instance it is a form of greeting much like the domestic cat’s meow which also has a variety of sounds or nuances depending upon the individual cat.
I have a page on the mountain lion whistle which covers similar ground, which you can read by clicking on this link.