Clarke, 33, is suffering from soreness in his left hamstring and did not train on Saturday ahead of the start of the one-day international tournament, which also involves South Africa.
Lehman said if Clarke did not recover in time to play at the Harare Sports Club, his place would be taken by Phil Hughes, who would open the batting with Aaron Finch.
“Obviously long flights don’t help the old fella,” said Lehman of the 36-hour journey from Sydney to Zimbabwe’s capital, where Australia arrived on Thursday.
“But he’s so professional in dealing with that sort of stuff, so it’s a little setback for us but it gives someone else an opportunity if he doesn’t come up. We’ll have to wait and see,” Lehman told a press conference.