Captain Michael Clarke has also stepped down from his role as a selector. The managerial changes come just 16 days before the start of the first Ashes Test.
Australia had won 10 of the 19 Tests under Arthur since his appointment in November 2011, but they have since endured a poor recent run of results including a 4-0 defeat to India.
The Aussies also crashed out of the recent ICC Champions Trophy without winning a single game.
"The timing is far from ideal but we didn't feel we could sit back and hope matters would change without addressing issues critical to a high performing team culture," read a statement from Cricket Australia CEO James Sutherland.
"It obviously isn't the type of change we want to make three weeks out from the Ashes commencing but we believe a change is needed."
Lehmann enjoyed a nine-year playing career for Australia in both Tests and one-day internationals before his retirement in 2005.