The UK's communications regulator received six complaints over the item on his BBC Three Counties Radio programme, which reportedly led to him leaving the show.
Ofcom said on balance the other party had an adequate opportunity to respond to Mr Lee, therefore no further action was necessary.
Libby Powell from the campaign group Christian Concern was invited onto the show to discuss the case of Revd Barry Trayhorn, a prison worker taking his employer to a tribunal amid claims he was forced to resign for reading a Bible verse about homosexuality.
Iain Lee said Revd Trayhorn was "obnoxious" and "poisonous" and said his views, and Ms Powell's were homophobic.
When Ms Powell said homophobia was a fear Mr Lee said it was a "cute answer" but homophobia was a "hatred of gays".
The BBC admitted the language the presenter used, and the tone in which he conducted the interview, was "at several points inappropriate".
A statement from senior editorial staff said: "The BBC - and Iain Lee himself - wish to apologise for any offence that may have been caused."
Iain Lee apologised on air and said: "Last week I interviewed the Revd Barry Trayhorn and solicitor Libby Powell about their understanding of biblical teaching on homosexuality.
"I want to make it clear that I apologise for any offence that may have been caused over the way I conducted the interviews."
Neither Mr Lee or the BBC have confirmed the reason for his departure but the presenter has hinted through his Twitter account that it was the interview which caused problems.