The fast bowler suffered an ankle injury in the first Investec Ashes Test at Cardiff which the hosts won by 169 runs.
Lehmann said Starc, who seven wickets in the match, will train over the next couple of days in a bid to prove his fitness for the Lords Test on Thursday.
The Australia coach told Sky Sports: “Hopefully he will have a bowl tomorrow or the next day and we’ll see how he pulls up.
“We’ll have to make a call pretty soon, we’ll wait and see.
“The big thing for us is he’s got to be fully fit, we can’t have a bowler go down.
“We might do [wait till Friday], we’ll sum it up tomorrow.”
Lehmann added if Starc is ruled out, Peter Siddle and Pat Cummins have the quality to step in.
“We’ve got some good depth in our squad.
“[Siddle] bowled really well for us in the tour games. He’s come into some form and was here playing for Lancashire.
“Him and Patrick Cummings give us some decent depth if someone falls over.”
The Aussies have been criticised for their performance at Sophia Gardens having started the series as firm favourites to retain the urn.
And Lehmann has vowed his side will raise their game for the second Test.
“We know what went wrong, we didn’t play well enough.
“We’ve got to get back on the horse and play as well as we can.
“A tight turnaround is good for us, the blokes are in good spirits.
“We’ll play better than we did in the last Test match, the boys are obviously hurting as you would do when you lose any game.”