No, based on the provided information, it is not stated that John and Lucy break up in The Rookie.
Understanding Lucy Chen's Relationships in The Rookie
The information available regarding Lucy Chen's character development notes a significant personal event: a breakup that occurred at Nolan's house in an episode titled "The Switch". This event is highlighted as part of Lucy's story, aligning with her journey as a police officer and her evolving understanding of her career commitment.
- Details of the Breakup: While a breakup is explicitly mentioned as part of Lucy Chen's narrative, the provided context does not specify that John Nolan was the other party involved in this particular separation. The focus of the information is on Lucy's personal growth, including her realization of commitment to her police career, which might have been influenced by her familial background where both her parents are psychologists.
- Scope of Information: The details confirm that a breakup involving Lucy Chen happened, and provide its location, but they do not establish or dissolve a romantic relationship specifically between John and Lucy. Therefore, the information provided does not support the conclusion that John and Lucy break up in the series.