Lycett, 17, Waddison, 16, and Lewis, 16, are heading to St George's Park this weekend.
Left-back Lycett has featured for the Pitmen's first team.
Attacker Waddison has been on the first-team bench, while centre-half Lewis is vice-captain of Hednesford's under-17s.
"It is a huge credit to the lads that they have earned this chance and it is a massive source of pride that Hednesford Town, a non-league club, is producing players of this calibre from its youth set-up," said Pitmen u17s boss Jaspa Jones.
"Hednesford really is the place to be for up and coming youngsters who want to firstly develop themselves as footballers and then go on to make a name for themselves in the game."