It has now emerged Mr Burns accused Lyons of “dragging his heels” on the project during the meeting.
He also challenged Lyons over his failure to attend any GAA matches.
One source said the talks at times were “fraught and tetchy”.
Lyons has attended a GAA event but not a match.
The minister has also insisted the Northern Ireland Executive will fulfil a previous financial pledge to support the Casement Park development.
It promised £62m while the Irish government has pledged more than £40m with the GAA offering a further £15m.
That leaves a shortfall of around £150m if the stadium is to be completed to the current price tag.
The GAA is now seeking a meeting with Secretary of State Hilary Benn to discuss the revised cost with a view to securing funding from the government.