David Pynn, head of Scalby school, Scarborough, made the proposal after calculating that his school budget will fall pound;50,000 short due to cuts of pound;2million to North Yorkshire's education budget.
Mr Pynn said: "We've lost two teachers as a result of budget cuts and face the prospect of further redundancies even though our school is over-subscribed and we have a very poor teacher-pupil ratio.
"Parents shouldn't have to top up what they pay for education through taxation with a donation. I know that some of them might not feel able to pay but it's only the cost of a lottery ticket after all."
Schools have come up with some novel ways of raising money. The head of Rush Common school, Abingdon, Oxfordshire, once spent half-term busking and performing in pubs, a primary school asked pupils to fill empty Smartie tubes with 20p pieces while a doctor donated his fees from vasectomies to buy toys for Waverley Street school, Nottingham.