。
She does whatever he tells her.
Literal
She [topic-は] his [genitive-の] doing-as-told is.
言いなり is a noun meaning 'doing as one is told, being a yes-man, being at someone's beck and call' — essentially submitting to another's commands without resistance. As predicate (彼の言いなりです) it describes a state of total compliance. The phrase carries a negative connotation in most contexts — implying loss of agency or unhealthy dependence. The polite です gives the sentence a slightly resigned, observational tone.