While there has been no official confirmation of the dismissal, it is understood that Arthur has been let go just weeks before the Ashes series with England.
"Perhaps we have made a decision that's going to head Australian cricket in the right direction," Lawson told BBC Radio Five Live.
"It's certainly an unusual thing for a cricket coach to be sacked so close to a major series. However, if it were a football coach, this would be minor news."
Darren Lehmann is expected to be named as his replacement in a press conference this afternoon.