Why is it important for the youth to participate in the lottery?

Via Merriam-Webster:

Indoctrinate: to teach (someone) to fully accept the ideas, opinions, and beliefs of a particular group and to not consider other ideas, opinions, and beliefs

The easiest way to indoctrinate someone is to start with a fresh slate. For humanity, there is no fresher slate than a child who, naturally, has very few preconceived notions of right or wrong, moral or immoral. The village in the story uses this to their advantage, even going so far as to state that "The children assembled first, of course." At the end of the story after Tessie Hutchinson is selected by the lottery, the narrator again points out the participation of the children by saying, "The children had stones already. And someone gave little Davy Hutchinson a few pebbles." The village has so successfully explained away the lottery that even the winner's (or perhaps the loser's from an outside view) children participate without protest.