He closed his bedroom door tight lest the sound of his tablet disturb his roommate.
He closed his bedroom door all the way, so the sound of his tablet wouldn't disturb his roommate late at night.
lest は古い英語でかたい言い方なので、ほとんど使うことはないです。どうしても使うなら、次のようになりますが、自然ではありません。
ーHe closed his bedroom door tight lest the sound of his tablet disturb his roommate.
「彼はタブレットの音でルームメイトを邪魔しないよう、寝室のドアをしっかり閉めた」
次のように言った方が自然です。
ーHe closed his bedroom door all the way, so the sound of his tablet wouldn't disturb his roommate late at night.
「彼は夜遅くにタブレットの音がルームメイトを邪魔しないよう、部屋のドアをしっかり閉めた」
ご参考まで！
He locked the door tightly at night lest the sound from his tablet leak out.
「彼は夜中タブレットの騒音が漏れない様ドアをしっかり閉めた」は英語で「He locked the door tightly at night lest the sound from his tablet leak out.」と言います。「lest」は「～しないように」の意味です。
彼は夜中運動の音が漏れない様ドアをしっかり閉めた。
He locked the door tightly at night lest the sound from his workout leak out.
カナダ 
