The Yorkshire side took the remarkable decision to sack Clark on Wednesday, with the team fourth in League One.
A 1-0 home defeat to Sheffield United on Tuesday night had seen them drop out of the automatic promotion positions.
"`This was a very difficult decision; one not taken lightly or in response to one result. Concerns have been raised over recent weeks," said chairman Dean Hoyle.
"Lee and his coaching staff have put their all into the job over the past three seasons and he has made a huge contribution to the club.
"However with 16 matches to go we still have an opportunity to achieve promotion and we have made this change with this in mind. Huddersfield Town would like to place on record it's thanks to Lee and his coaching staff and wish them all the best for the future."
Lillis returned to Huddersfield, for whom he played, in December as head of their academy.