。
The news of her lover's death deeply disturbed her.
Literal
Lover [of-の] death [of-の] news [at-に] she [topic-は] greatly heart [object-を] disturbed.
心を乱す ('to disturb one's heart') is an idiomatic verb phrase for being mentally agitated, distressed, or thrown off balance. The に on 知らせに marks the cause/trigger ('upon hearing the news,' 'at the news'). 大いに is a higher-register adverb meaning 'greatly, considerably,' more bookish than とても.