In recent months, there has been a surge of public anger over pay deals awarded to performers and executives at the BBC. In response, Lyons has ruled out "excessive salaries" for BBC senior staff and talent.
The BBC's director general, Mark Thompson, is likely to publish a strategic review next month to reassess the size and shape of the BBC.
The review, being published two years ahead of the next licence fee settlement, has raised suspicions that it is designed to head off political interference before the general election. However, Lyons has denied this.
In the wake of rumours that the Trust would be one of the first causalities of the Tory government, he said that the trust is not going to be bullied.
He blamed the relaxed culture at the BBC in the early 2000 for its current troubles.