。
She told me I could use the dictionary.
Literal
She [topic-は] me [to-に] dictionary [object-を] use [permission-てもよい] [quotative-と] said.
An indirect quotation of a permission grant. ~てもよい (or ~てもいい) is the standard 'it's okay to / you may' permission frame, formed concessively as 'even if [you] X, it's good.' よい is the more formal/written register cousin of いい — interchangeable in meaning. The whole permission statement is then quoted via と and reported with 言う.