Anderson has led the Giants to the League Leaders’ shield in his first full season in charge since succeeding Nathan Brown at the John Smith’s Stadium.
They host Wigan in the first round of the play-offs on Thursday, knowing they are potentially just two wins away from the Grand Final at Old Trafford.
Lunt told the club’s official website: “Paul has been fantastic, he really has. He’s won everything as a player himself, played for all the top teams and Great Britain as well, so if anyone knows how to keep cool and play these games it’s Paul Anderson.
“I’ve played five seasons here now and I consider Huddersfield my home from home, so it would be brilliant to help them claim the Super League Trophy, not just for me, but for the team, the fans and for Ken Davy.
“But again, we can’t allow ourselves to think too far ahead. We’ve got Wigan Thursday, so we’ll just focus on the immediate game ahead.”
A win on Thursday would give Huddersfield the luxury of a week off, and the ClubCall pick for the semi-finals.