The 38-year-old offspinner was not on the team sheet for the second Test at the Gabba, with seamer Michael Neser preferred in an all-pace attack.
To compound his forgettable day, Lyon was struck on the ankle while bowling to teammate Beau Webster in the nets during the lunch break.
He was seen in discomfort, but the Australian camp confirmed there were no injury concerns.
Pat Cummins did also not quite make the cut, but Bailey said he would be fit to play in Adelaide.
The last time Lyon was omitted for a home Test was in January 2012 at the WACA against India.
He had played 71 home Tests in a row before being controversially left out.
Australia's chairman of selectors Bailey revealed Lyon's displeasure after selectors chose Josh Inglis and Neser ahead of Beau Webster and Lyon.
"I don't think he agreed with it and that's fine," Bailey said.
"I think Beau Webster is in the same boat, that (omission) was heavily debated.
"Nath will disagree with the decision and that's perfectly okay. I think he disagreed with the decision in Jamaica.
"There's no qualms about players feeling like they can impact the game."
When Lyon was omitted for the third and final Test in the West Indies earlier this year, national selector Tony Dodemaide also said it was "a one-off".
Bailey was emphatic about Lyon playing the third Test.
"Very much it's a one-Test decision. Nath will play in Adelaide," Bailey said.
"It's just how you think you're going to structure up the resources and how it's going to be used when it gets dark, when you think you're going to be using seam bowlers, how many bowlers get used in a day, when you think the new ball is going to be available, that sort of stuff."
Bailey added there were "a number of factors" at play.
"I wouldn't like to be going down a path where you're saying it's purely the wickets or purely the way the game's been played and certain games not going as deep into days four and five," he said.
"It's probably just highlighted with Gaz because there's been years where he has (bowled a lot) and his ability to bowl long spells, go at two an over and do that sort of stuff. It just hasn't quite panned out that way."
Bailey said the decision for Cummins not to play was made on Wednesday night.
"He could've played but there would've been some restrictions around the overs," Bailey said.
"Probably the key factors were what does that look like for post-this and are you accentuating that risk going forward and what are the uncontrollables in the game and does that put other players under pressure?
"It's one where we can't budge. There was going to be a hard number of overs."
Cummins has made outstanding progress from a back injury and will only be in a better condition by Adelaide.
"Now he's into that mode where it's back-to-back bowling days," Bailey said.
"It's one of those ones where the longer (recovery) the better."
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