Clarke, troubled by a third hamstring setback since August, ran at the Sydney Cricket Ground on Friday before heading to Adelaide to join the Australia squad later in the day.
The skipper, who was one of the pallbearers and led the tributes at the funeral of his close friend and Test batsman Phillip Hughes on Wednesday, will be given every chance of taking the field in the series opener against India at the Adelaide Oval on Tuesday.
“As long as he’s fine to do the running and can bat (he’ll play),” coach and selector Lehmann told reporters on Friday.
“He flies in this afternoon. We’ll get him batting tomorrow and see how he goes.
“It’ll be case of if he’s fine, he’ll play. We’ll just have to wait and see.
“We’ll be guided by medical staff, the captain himself, selectors. We’ll get together and assess what the plan is tomorrow.”
Clarke and the entire Test squad attended Hughes’s funeral in Macksville in northern New South Wales on Wednesday.
On Thursday, Clarke attended a private cremation service with Hughes’ family in their home town while his teammates began to make their way to Adelaide.
“He’s pretty mentally strong, as you saw throughout the week,” Lehmann said of Clarke should he lead Australia in what is shaping up as an emotional Test.
“He held himself together really well and led the team really well.”
Batsman Shaun Marsh has been added to Australia’s Test squad as cover for Clarke.
Lehmann said it was too early to speculate who would be emotionally ready to start the Adelaide Test, given the traumatic lead-in to the series.
“Time will tell, but today we’ll get out there and see how we go,” he said prior to Australia’s first training session since Hughes was fatally struck by a bouncer in a domestic game.
Hughes, 25, died last Thursday from bleeding on the brain, two days after being knocked unconscious by a bouncer in Sydney, throwing the cricketing world into mourning.
“Now it’s a matter of rallying around each other, rallying around his family and the whole CA (Cricket Australia) family,” Lehmann said.
He said he wouldn’t expect Australia to be trained at full intensity for a few more days.
“Probably not today, but certainly by the weekend. By Sunday or Monday I’d expect them to be going 100 percent,” he said.
Murali Vijay, stand-in skipper Virat Kohli and Rohit Sharma all attended the Hughes funeral and were all playing in India’s final pre-Test tour game against a Cricket Australia XI in Adelaide on Friday.