Ross was suspended from his shows for three months after he and comedian Russell Brand left lewd messages on the voice mail of 78-year-old "Fawlty Towers" star Andrew Sachs during Brand's BBC Radio 2 show last month and the segment drew widespread criticism.
Brand, Radio 2 head Lesley Douglas and David Barber, the executive who cleared the stunt for broadcast, resigned.
"It is not the job of the trust to make decisions about the terms and conditions of performers or the sanctions that are applied to them," BBC News quoted Lyons as saying. "We are very clear that the director general has taken the right action with respect to Jonathan Ross. ...There is a slippery slope in responding to pressure. Where does it end? It starts with comedians, and it ends with making judgments about who presents the news."
BBC trustee Richard Tait said Brand and Ross weren't the only ones to blame in the incident.
"It was a very offensive program which should never have been recorded," Tait said. "Once the offensive phone call was made, the recording should have stopped and senior management alerted. It is a catalogue of editorial and management failures."