Lady first encounters the rat while she is running happily in the backyard. She sees him, growls, and chases after him, causing him to scamper through a hole in the fence.
The rat has a catalytic role in the climax of the film when he comes back to Jim Dear and Darling's house through the fence hole, while Lady is tied to her doghouse on a rainy night. She barks at him, but Aunt Sarah tells her to shush. Tramp hears her barking and comes back to her, where she tells him that there's a rat in the house. He then follows him to Jim, Jr.'s room, before he can harm the baby. They engage in a fight, until at one point, he climbs to the top of Jim Jr.'s crib, looking to escape. Tramp chases him off while overturning the crib by accident, waking Jim Jr., and making him cry. Finally, Tramp manages to corner the rat behind the couch and kill him.
Having been alerted by the commotion, Aunt Sarah arrives and, not seeing the rat, mistakenly believes that Lady and Tramp had attempted to harm Jim Jr., promptly locking Lady in the cellar and sending Tramp off to the pound. However, as soon as Jim Dear and Darling return, Lady shows them the dead rat, clearing Tramp's name.
In an early script, the rat's name was Herman.
Additionally, in the same early script, Lady was the one who fought the rat.