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She supplements her income by taking in student lodgers.
Literal
She [topic-は] students [object-を] cause-to-lodge [so-て] income [object-を] is-getting.
下宿させる is the causative of 下宿する ('to lodge / board'), so 下宿させる literally 'cause [students] to lodge' — meaning 'take in lodgers / put students up.' The te-form 下宿させて links the causing-to-lodge as the *means* by which she gets income. 下宿 itself refers to a long-term boarding arrangement, traditionally common for university students living away from home in a private residence (different from a 寮 dormitory). The verb 得る (read here as える, sometimes える/うる depending on dialect) is the slightly literary verb for 'obtain / gain.' The whole sentence depicts a quietly entrepreneurial older woman, a recurring figure in Japanese fiction and real estate.