。
She has a lot of English-language books.
Literal
She [topic-は] a-lot [genitive-の] English [genitive-の] books [object-を] [has-持っています].
英語の本 ('English books') uses 英語 attributively with の to mean 'in English' as a noun modifier — 'English-language books.' Compare with 英語が上手 ('good at English'), where 英語 is a が-marked argument, and 英語で書かれた本 ('books written in English'), where 英語で is an adverbial. The の in たくさんの本 is required because たくさん modifies a following noun; without の it would have to be adverbial as in 本をたくさん持っている. Japanese learners often own a private library of English material — anything from textbooks to novels — and the sentence reads naturally in that learner-life context.