A Cayman lottery is an easy option and will give some relief to the government.
It is, if carefully handled and by allowing visitors to gamble too, at say a higher tax rate, a possible addition to the easing of financial constraints.
The chance of winning a sum that could be the cost of a holiday back would be a good incentive. I am advocating a two-tier system and a three-way share of the cherry. The third piece is the tax bite. Good placement is the key.
I wish you luck.