Under-18s boss Lunt, 37, who made 436 appearances as an Alex player, mostly between 1997 and 2006, is promoted to assistant manager, following Sunday's sacking of Steve Davis.
Alex Morris has been given the job of first-team coach, but will also continue as Under-23s manager.
Head of recruitment Neil Baker will be more involved in first-team matters.
James Collins, assistant manager under Davis, has been offered the role as head of coaching for the academy under director Dario Gradi, who is still subject to an Football Association interim suspension.
"Kenny's going to assist and Alex is going to work very closely with us," Artell told BBC Radio Stoke. "And I want to lean on Neil like a lamp-post. I'm waiting to see how much of a part he wants to play.
"If you know how to win, that's 80 per cent of the battle. But knowing what to do doesn't always translate to knowing what to do as a manager. It's all about getting that experience and I'm going to make mistakes.
"I'm a magpie. I think that's one of my strengths. I'm also going to bleed people around me of their knowledge. Whether it's Kenny, Alex, James Collins, Neil Baker, or Dario, if I have that opportunity in the future.
"Between us, with my man management skills, their coaching ability and mine and Kenny's dressing room experience and knowing what it takes to succeed, we've enough about us to drive the club forward and repeat the success that the previous incumbent had early on in his career at Crewe."
Artell has taken over a Crewe side 18th in League Two, just seven points clear of trouble, having won just twice in 21 matches since mid-September in all competitions.
Crewe have named former player Kenny Lunt as assistant manager in a backroom shake-up under new boss David Artell.