Muralitharan has undergone shoulder surgery and will be out of action for at least four months, meaning he will also miss the Champions Trophy and a tour to Pakistan in October.
Sri Lanka have expanded their squad to 15 players, which will allow them to have a closer look at Herath and Lokuarachchi before finalising Muralitharan's replacement for the Champions Trophy in England next month.
Lokuarachchi, 22, returns to the one-day squad after a fine tour to England with Sri Lanka 'A', while Herath, 26, has been on the fringes of the squad since making his debut against Zimbabwe earlier in the year.
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"Obviously the loss of Murali leaves us with big shoes to fill, but we drew a Test without him in Australia and we won against South Africa without him," Dyson told Reuters.
"The guys are starting to feel that they can perform without him and until he returns this is a great opportunity to prove that."
Sri Lanka, who won the Asia Cup earlier in the month, and completed their first Test series win over South Africa on Sunday, kick off the one-day series under lights at Premadasa International Stadium on Friday.
Sri Lanka squad:
Marvan Atapattu (captain), Sanath Jayasuriya, Kumar Sangakkara, Mahela Jayawardene, Tillakaratne Dilshan, Saman Jayantha, Avishka Gunawardene, Farveez Maharoof, Chaminda Vaas, Upul Chandana, Lasith Malinga, Nuwan Zoysa, Dilhara Fernando, Rangana Herath, Kaushal Lokuarachchi