She lived happily.

Literal

She [topic-は] happily lived.

幸せに here is the adverbial form of 幸せ used with に, modifying the verb 暮らす ('to live, spend one's days'). Compare 幸せに暮らした with classic fairy-tale endings: '...and they lived happily ever after' translates naturally as ~は幸せに暮らしました or its eternal variant ~はいつまでも幸せに暮らしました. Japanese fairy tales (昔話) often end with めでたしめでたし ('all is well that ends well') as a closing tag.