Hi. As far as I know 寝転がる is 五段動詞 so its passive form should be 寝転がられる. But in this sentence, it is 寝転がされる. I wonder why? Besides, why is passive form used here? He was lain down?
That's "寝 + the passive form of 転がす". 寝 would be the -masu stem of 寝る, which is used to make a compound verb (e.g. 食べ残す, 飲み終わる, はじけ飛ぶ, etc.). This is also the etymology of 寝転がる.