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You're right, there'll be a similar effect. With premium bonds this is because the smallest prize is £25. (So if 25 people stick in £100, all expect £1 but only only of them actually gets the £25 prize and median prize is £0.) I thought you could win smaller prizes on the lottery which would reduce the effect. Just had a look and it seems the lowest two prizes are "free lucky dip" and then £30. Does the free lucky dip mean another entry into the same draw? Because that's interesting if so and will make the calculation recursive and horrible.
it will be <0% but would interesting to see exactly how much