Such a lottery can be had.
If there is an epsilon chance that a given lottery ticket is a winner,
there is also an epsilon prime chance that a winning ticket will be lost and that you will find it, for zero dollars expenditure on your part.
Thus, there is an epsilon multiplied by epsilon prime chance that you will be a lottery winner without actually buying into the lottery.
If you get your hopes up for this scenario, are you a free-loader?