The reigning Scottish champions were expected to collect all three points from their trip to strugglers Ross County, but failed to take the chances they created, while they were then stung when the hosts scored in the 71st minute through a Jordan White header.
Celtic had no answer and their rivals Rangers are now just seven points from clinching the Scottish Premiership title.
For Bonner, who feels Lennon is on borrowed time, there is a lack of leadership and he is keen to see the board plan for the future soon.
“Neil Lennon knows it himself that he’s on borrowed time”, Bonner said on BBC Sportsound.
“He was playing for his credibility from now to the end of the season.
“But it’s all about the leadership and what decisions they make at a board level.
“They need to come out with a clear plan soon.”
Celtic are now 18 points behind Rangers and Steven Gerrard’s men just need to pick up seven points from their eight remaining games to secure the title.