This is actually already a thing. Rather than lottery pools, companies have a collection where people can contribute every week, and at regular intervals it 'pays out' to one person in the pool. Everyone wins in turn, it's effectively gamifying saving money, combined with the pooling aspect of corporate lottery buying. It's much more profitable than buying lotto tickets on average, because there's no outflow. In addition, the money can be stored in a short-term security, like a monthly rotation of one-year GICs. This requires more overhead to get started, but then you actually turn a small profit.

That said, I don't know if you could start a company around it. Most of the point is the social aspect of collecting the money and deciding who 'wins' for a given week ( I suppose you'd do a lottery from a pool where winners aren't re-entered)