Former Cosatu general secretary Zwelinzima Vavi and EFF leader Julius Malema are plotting to overthr.
His resignation came after the Premier Soccer League rookies' 2-1 loss to Lamontville Golden Arrows at Peter Mokaba Stadium on Sunday.
Rise and Shine lost their opening match of the season 1-0 against Maritzburg United in KwaZulu-Natal and went on to lose 3-2 against Bloemfontein Celtic at home, before going down 2-1 to Platinum Stars away.
Last week speculation was rife that former Orlando Pirates striker Ian Palmer was being lined up to replace Lechesa.
Club boss Johnny Mogaladi could not be reached for comment yesterday.
Lechesa joined the Polokwane outfit in January, when they were still in mourning after four of their players were killed in a car accident on their way home from a league match in Mankweng. He guided them to the PSL by finishing top in the National First Division.
Lechesa, who was the youngest coach in the PSL at the age of 37 before leaving the club yesterday, replaced Serbian Vladislav Heric.
"I can confirm that I have left Polokwane City for personal reasons. That is all I can say at the moment," said Lechesa yesterday.
Team manager Bernard Molekoa is expected to be named caretaker coach while the club searches for Lechesa's replacement.