Lyon said a phonecall on Thursday telling him of the departure was the first he knew about it having left Canberra with no indication that Saker was about to quit.
Head coach Justin Langer said there were "numerous reasons" for Saker leaving and that discussions over his role had been going on since Langer took on his job following the fallout to the ball-tampering scandal.
"I was shocked by it to be honest, I'm a bit disappointed," he said. "I was taken aback. I didn't really catch on about anything in Canberra after a great Test win, I didn't think anything of it and he didn't mention anything to me. I'm not part of those conversations between the coach and management but he's been great for me, a massive support, so he'll be missed for sure."
It has been noted how Mitchell Starc credited New South Wales bowling coach Andre Adams after his return to form in the second Test against Sri Lanka, but Lyon said he was speaking on behalf of all Australia's bowlers when he lauded Saker's role.
"I really enjoyed working with David and I know I'm talking on behalf of the all the fast bowlers as well. But it is what it is, he's got my support, but I'm not part of those conversations behind closed doors. We'll just have to crack on and make sure we get our bowling plans for the World Cup and Ashes down pat."
Troy Cooley, the National Cricket Centre coach and former England and Australia bowling coach, will fill the role on an interim basis for the limited-overs tours of India and the UAE against Pakistan.
Australia will be without Starc for the series in India after he suffered a pectoral muscle injury in Canberra which has given an opportunity to Kane Richardson. Pat Cummins, who has been elevated to ODI vice-captain alongside his Test role, is the only one of Australia's main three quicks to make the India trip with Josh Hazlewood still nursing the back injury which ruled him out of the Sri Lanka series.
"It's disappointing for Mitchell to miss a tour but we've got some quality quicks in that group - Nathan Coulter-Nile coming back, Jason Behrendorff, Kane Richardson, Jhye and Pat Cummins - so there's enough quicks to stand up and push a claim for a WC berth. No doubt Mitchell will be right for the World Cup," Lyon said.