Lukas Gage Shades Chris Appleton in Exes' Book Battle

Lukas Gage is reacting to his ex-husband Chris Appleton announcing an upcoming self-help memoir on the heels of Lukas' upcoming book ... and it sounds like he's throwing some shade.

We got the actor outside DOGPOUND Gym in West Hollywood on Monday and our photog asked him about Chris recently announcing a self-help memoir.

Lukas says he didn't know about it but feels "honored" to be so "influential" with the timing of his ex's book.

LG's book, "I Wrote This For Attention," is due out in October and Chris' "Your Roots Don't Define You," drops in January ... just 3 months after Lukas'.

We asked Lukas some follow-up questions, but it seemed like he didn't want to take any more perceived shots at Chris ... though he may have sarcastically said the timing was "coincidental."

This is on par for Lukas ... he seemingly threw some shade at Chris last year with a comment about dating apps, but then clarified there was no ill intent.

Sources with direct knowledge tell TMZ ... Lukas, and people on his team, aren't happy about the timing of Chris' book release.

We broke the story ... Chris, a celebrity hairstylist who works with the Kardashians, filed for a divorce from Lukas back in November 2023 after only 6 months of marriage. The divorce was finalized in June 2024.

Lukas isn't sure if he's getting name-dropped in Chris' book ... and we also asked about how things stand between them ... check out the clip.