The Glasgow giants have endured a torrid season so far on and off the field with the fans taking aim at the board for a perceived lack of investment in the playing squad.
Lawwell joined Celtic as chief executive in 2003 and served in that role until 2021.
The 66-year-old returned as non-executive chairman in 2023.
"It is with sadness that I announce my decision to stand down as chairman," Lawwell said in an emotional statement on the club's official website.
"I believe that my 18 years as chief executive and three years as chairman have shown my ability to meet and overcome challenges on many fronts, but abuse and threats from some sources have increased and are now intolerable.
"They have dismayed and alarmed my family. At this stage in my life, I don't need this. I cannot accept this and so I leave the club I have loved all my life."
Non-executive director Brian Wilson will become interim chairman from 31 December until a permanent appointment is made.
Celtic have won 13 of the last 14 Scottish Premiership titles but have suffered a dramatic dip this season.
The Hoops suffered an embarrassing Champions League qualifying exit to Kazakh champions Kairat Almaty.
Brendan Rodgers departed as manager in October amid acrimonious relations with the board.
And new coach Wilfried Nancy is off to the worst start of any boss in Celtic's history with three consecutive defeats, including the League Cup final against St. Mirren on Sunday.
Large sections of the Celtic support have consistently chanted for boardroom change at matches in recent months.
The club have also indefinitely banned the prominent supporters' group "The Green Brigade" from attending matches, citing safety concerns.