She lived in that town her whole life.

Literal

She [topic-は] lifelong that town [in-に] lived.

終生 (しゅうせい) means 'throughout one's life' or 'lifelong' — a formal, literary adverb. The simple past 住んだ reports the completed fact of her having lived there. その町に住んだ uses に with 住む to mark the place of residence. The finality of the statement — she lived there, and her life is over — gives this sentence a quiet, reflective quality, as if summing up someone's existence in a single line.