The design for Lola was originally designed by Howard Stark and was exhibited in the early days of the Stark Expo (though its power to fly was not operational yet).
Lola originally premieres in the pilot. Coulson is incredibly protective of his car, even telling multiple people not to touch Lola. At the end of the episode, however, he reveals to Skye that Lola has the ability to fly.
Throughout the first season, Coulson often drives Lola on missions.
In "Nothing Personal", when Coulson is saving Skye from the HYDRA agents who have taken control of the Bus-Ward and Deathlok-he must escape from the cargo hold without having to confront Deathlok. He opens the bay door and drives Lola out. They plummet until Coulson is finally able to activate the thrusters to allow for flight. They land safely on the ground.