Before you start emitting samesite=lax, be warned that webkit/safari iOS12 has a weird implementation: if you set the cookie in a POST method and redirect to a GET (like most default oauth explicit grant login flows), the cookie will not be sent: they consider POST pages as "unsafe". See https://bugs.webkit.org/show_bug.cgi?id=188165#c12 for more details.

Edit: it looks like people have found other issues since I last looked at this bug:

> It's a serious issue affecting many common user flows, including the flow of visiting a website coming from a GMail link. If the user comes from GMail, it reaches the destination website without any cookies, thereby breaking functionalities that depend on session/login cookie and CSRF cookie. Only fix for now seems to be removing the Lax flag from cookies. (https://bugs.webkit.org/show_bug.cgi?id=188165#c47)

At this point, it looks like the safest approach is to only emit sameSite if the browser isn't safari.