Jayasuriya will replace Muralitharan at the county when the off-spinner returns home this week for the three Test matches against Bangladesh starting on June 25.
And Muralitharan will go back to Lancashire after the series ends on July 24 as Jayasuriya returns to take part in the three one-day internationals against Bangladesh.
Jayasuriya's stint with Lancashire came about after the national selectors told him that he would be rested for the Test series to allow former captain Marvan Atapattu to make a comeback.
"I will go to Old Trafford to replace Murali till mid-July", Jayasuriya told reporters here on Wednesday.
Jayasuriya had earlier played county cricket for Somerset in 2005.
He said he would be playing eight Twenty20 games, a Sunday League one-day match and one county championship game for Lancashire during his month-long visit.
Chaminda Vaas and Kumar Sangakkara, two other Sri Lankans playing in county cricket, will also return for the Bangladesh Test series.