Australia are 1-0 down in the series and desperately needing an improved performance from their batsmen in the second Test starting on Thursday.But regardless of selection for the second Test, Warner looks set to return to the side for the third Test at Old Trafford, if he can make runs for Australia A against Zimbabwe and South Africa A.
Cowan's average has slipped to 31.28 from 18 Tests, after two irresponsible dismissals at critical times in Australia's agonising 14-run first Test loss at Trent Bridge.
Lehmann has made it clear batsmen need to score runs to keep their place in the team.
"We've told Ed how we want him to play and how we want him to bat. That certainly hasn't changed from when he first come into the side, I wouldn't think," Lehmann said.
"We picked him to do a role. He'll be disappointed with the shots. So are we. That's just part and parcel of what we're about.
"He had a tough game. Like everyone's position, you've got to make runs and perform."
When asked how Australia would respond in a four-day turnaround from one of the most gut-wrenching defeats in Test history, Lehmann said the boxing kangaroo would keep on fighting.
Even if Warner's indiscretion in a Birmingham nightclub last month made his choice of words a source of mirth for reporters.
"We're going to keep punching aren't we ... I shouldn't use that. I do apologise, that slipped out," said a blushing Lehmann.
"No, we'll keep going. We'll just keep coming back at them all the time.
"We've just got to capture those key moments. And I think if you look back on the game, we've certainly got to bat better as a top order. That's the key."
Warner averages 39.46 from 19 Tests with three hundreds, and if not for his suspension, would have lined-up in the middle order at Trent Bridge,
The 26-year-old remains central to Australia's plans for the future.
With runs under his belt, he will eventually be given his shot at No.6, with Phil Hughes likely to move back to No.3 - and this could happen as soon as the third Test at Old Trafford, with Warner set to return from Africa several days beforehand.
Top order batting collapses in both innings of the first Test were only partially masked by wonderful 10th wicket partnerships putting on 163 and 65 respectively.
Australia's final wicket stands have averaged 40 since the beginning of last year, which would be a more significant bonus if Michael Clarke wasn't the only batsman averaging more than that in the top order.
"It's time for the batters to make sure they're making the runs and giving the tail a bit more time," said Lehmann.
"I think we only batted for 65 overs in the first innings and 111 today. We've got to be reversing that.
"I don't like tinkering with techniques too much, as a coach. It's more about getting a game style you want them to play to particular bowlers ... and certain situations."