The Saints are reportedly preparing one final contract pitch to Battle, who is in Hawthorn's sights.
A beefed-up offer could mean St Kilda retain the 25-year-old free agent's services or force the Hawks to increase their bid, ensuring the Saints secure a first-round draft pick as compensation.
"Josh has invested a lot in us, we've invested a lot in him, but I just let it play out," Lyon said on Friday.
"He's playing great footy, we have a strong relationship, but at the end of the day it's a professional environment and there's mechanisms that people either avail themselves of or they don't.
"That'll all wash out but I'm really focused on the game (against Carlton on Sunday), as is Josh."
Pressed on which way he thinks Battle is leaning, Lyon said: "I've got not idea. I know he's focused on training - that's the idea I have."
Lyon said Battle received votes in the Saints' best-and-fairest award last week for his role on Jeremy Cameron, and will have another big job against Carlton at Marvel Stadium.
The Blues will be without injured star forwards Charlie Curnow and Harry McKay as they chase a result that would guarantee them a finals spot.
St Kilda's comeback win over finals-bound Geelong was the fifth victory in their past seven games, in an improved run of form through the second half of the season.
"Ross gave us a bit of a bake at half time. We probably deserved it."— 7AFL (@7AFL) Rowan Marshall, understandably, is stoked with that response 🔥#AFLSaintsCats pic.twitter.com/UY8ZqdEPnGAugust 17, 2024
But the clash with Carlton will bring their campaign to an end, with the Saints (10-12) failing to repeat last year's promising finals appearance.
"There's disappointment, obviously, but I don't think it changes what we were doing," Lyon said.
"There's been a lot of wins, a lot of youth, a lot of debutants again this year.
"Close losses we learnt from and I think the good thing is where we were stuttering, we've taken some great lessons on different aspects of our game and improved it.
"And we know when we can get our midfield right, a lot of the other pieces are in place."
Lyon said second-year Saint Mattaes Phillipou will play through the midfield against Carlton on return from two weeks out of the side because of illness.
Anthony Caminiti is out of the side because of a shoulder injury.
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