Robins' tenure at the Championship side came to an end after a 4-0 home defeat to Bournemouth on the opening day of the new season.
Lillis, the club's academy manager, will step up and look after first-team duties while chairman Dean Hoyle sources a long-term replacement.
The 54-year-old previously assumed charge prior to Robins' appointment in February 2013.
After the poor start to the campaign, Lillis has called on everyone at Huddersfield to pull together and work on turning their fortunes around quickly.
"As a club – staff, players and fans alike – we have to pull together and move on," he said.
"We have a Capital One [League] Cup game at Chesterfield on Tuesday, which is an important one for the club and players after the performance and result on Saturday. We must go into the cup game to win and play how we can. A win could kick off a run.
"I know that the fans will get behind the players if they put a shift in and we've challenged the players to do that."
Lillis, who started his playing career at Huddersfield, will be assisted by Steve Thompson and Steve Eyre.
