She went looking for her lost child.

Literal

She [topic-は] lost-child became own child [object-を] search [purpose-に] went.

迷子になった自分の子供を捜しに行った — 捜す (さがす, alternate kanji for searching for people) with に行った marks the purpose of going. 自分の ('one's own') emphasizes it's her child.