'The idea was borne out of frustration at the enormous financial pressures put on local government,' said Mr Bennis. 'The government has squeezed us so much the pips have fallen out.
'It is not unreasonable to spend £5 a week when you look at the benefits which could be achieved,' he said. 'I am not suggesting we should send the chief executive to the horses or a casino.'
Mr Bennis, who is an entertainer by profession, proposed the chief executive be given the power to choose the numbers.
The DoE confirmed councils had no power to gamble.
A spokesman said that in theory any winnings would either be subject to capping or treated as a windfall and used to reduce local council tax.
He is also looking at the possibility of establishing a voluntary lottery fund which would be under council control.