I'm guessing because ležet is an imperfective verb (nedokonavá). So it expresses an action that is ongoing. Lehnout is a perfective, so the "lies" version in Czech could be "Jeho kočka si lehne u okna."
Czech native, please correct me if I got the above wrong.
In English, in the present tense, "laying" would only be used in the context of a bird laying an egg, or highly similar context. Here is is incorrect, it must be "lying". However, in the past tense, you could say either "the cat was lying by the window" or "the cat lay by the window".