Recumbent refers to lying down. I think of recumbent bicycles and recumbent statues when I hear this word. It can refer to a person as in this passage: … the psychiatrist's popular image remains that of a little bearded figure with a Central European accent, scribbling away in a notebook behind his recumbent patient. —Roland Littlewood, Times Literary Supplement, September 1984 But as you can see, it simply means that the patient is lying down, she is not being lazy. I applaud you for thinking outside the box and trying out new words. Good job. As Colin suggested, it's not a common word to use in everyday English.

No, they don't have the same meaning. Recumbent means lying back or in a very relaxed position; I rarely use this word, though it is seen in novels, and occasionally used for added irony in real life. I'm sure you know the meaning of lazy.