"SameSite=none" does not work with iframe
I think you should ensure that SameSite flag is always set to None for those cookies. If it's initially set to Lax, and then you try to make it None, it may not work.
Also, you should ensure that Secure flag is always set to true for SameSite=None cookies.
It works for me, setting cookie via PHP;This is a HACK for php < 7.3 (!)
session_set_cookie_params(3600*24, '/;SameSite=None', $_SERVER['HTTP_HOST'], true);
(secure = true is important)
In case of hosting in IIS you can add below configurations in web.config to avoid adding SameSite=Lex by browser
<sessionState mode="InProc" **cookieless="UseCookies" cookieSameSite="None"** timeout="20"/>