The 24-year-old was offered fresh terms with the League One club at the end of last season but has opted against staying at Ashton Gate and will play his football elsewhere next term.
Head coach Sean O'Driscoll told the club's official website: "Lewin was offered a new contract at the end of the season. Then that wasn't signed and we got Derrick Williams - another left-sided defender with Liam Fontaine also under contract.
"Can we justify a third one? It's a difficult one. I'd personally like to keep Lewin, but from a financial point of view and trying to balance the squad out, three left-sided centre-backs doesn't make much sense.
"There is no deal to be done and we expect Lewin to pursue his career elsewhere."
Meanwhile, O'Driscoll has played down reports linking the Robins with a swap move involving Paul Anderson and Ipswich forward Jay Emmanuel-Thomas.