The issue was put under the spotlight again when Bancroft last week revealed that Australian bowlers in the team at that time might have had some knowledge about the plot.
Bancroft, who had the sandpaper in his possession, was suspended for nine months for his role in the ball tampering plot during the Cape Town Test.
Both Smith and Warner were introduced to the new culture of team, when they spent time with the squad in the UAE ahead of the concluded five-match ODI series against Pakistan.
Television footage of the scandal-hit third Test in Cape Town showed Lehmann relaying a message down to Handscomb after cameras caught Bancroft attempting to alter the ball's condition.
Cricket Australia today banned Smith and David Warner for one-year while Cameron Bancroft was given a nine-month ban after the board completed its investigation into the ball-tampering scandal.
Bancroft was caught on camera using a sand paper to rough up the ball and Smith later admitted that it was a pre-meditated move thought through by the team's leadership group.
Warner, along with Australian skipper Steve Smith and opener Cameron Bancroft, are in the line of fire due to the scandal that broke out during the third Test against South Africa in Johannesburg.
Lehmann was hailed as a saviour when he took over in 2013, but critics now accuse him of overseeing a toxic culture that has dented the reputation of the famed Baggy Green cap.
Warner has also removed himself from a WhatsApp group comprising Australian players, with one source saying he has "gone rogue" since the ball tampering saga broke.
Australia ball-tampering scandal: ICC suspends captain Steve Smith for one match, Bancroft handed three demerit points
Smith, who stood down temporarily as captain of the team on Sunday, will now miss the final test of the series against South Africa in Johannesburg.
South Africa was 333-7 in its second innings at lunch, a lead of 389 and poised for a big win and a 2-1 series lead.