She warned in a statement on the foundation's website that the group was thinking about terminating its covenant with the foundation.
The foundation has rejected a new interim funding proposal from Lloyds, which says it has made "significant losses" during the recession.
Under the proposed deal, the foundation's share of the banking group's pre-tax profits would be cut from 1 per cent to 0.5 per cent. The group also wants to place a senior banking director on the board of the foundation, which has been providing about £6m a year for communities and charities in Scotland.
Craig wrote that there could be no reading of the move other than that "the group is not getting its own way in forcing us to accept terms not in the best interest of the charities we support".
In a letter to the banking group, Martin Sime, chief executive of the Scottish Council for Voluntary Organisations, said it was "time for the banking group to set aside its unwelcome proposals and to support the crucial activities of the foundation with renewed intensity".
A spokesman for the Lloyds Banking Group said "its door remains open to the foundation and will remain so for the foreseeable future". He said its proposals guaranteed the foundation almost £7m a year over the next four years, "with its independent status remaining very much in place".