I have a small LTI application that integrates with canvas, and after the LTI launch I can't access the cookie. This is failing in Safari (always) and Chrome (sometimes).
I am forcing the SameSite=LAX field of the cookie.
I'm not sure what else I should try.
There have been numerous changes in Chrome (and other browsers) regarding cookies and iframe.. For LTI 1.3 launches this is extra difficult because of how you need to track the state of the launch in the cookie while processing the OIDC flow.
The basics of what is changing is there is now a 'SameSite' cookie policy, where Only cookies set as SameSite=None; Secure will be available in third-party contexts, provided they are being accessed from secure connections. So marking the cookies as Secure and HTTP-Only is a must in addition to the SameSite=None
Also in Safari, the third-party frame will have to request access to the storage API before the cookie will be accessible.
Firefox is using a partitioned approach to the storage, and so the frame will behave as normal unless you then open your application as a new window then the cookie store may or may not follow depending on how the new window was created.
Cookie Status is an excellent resource to track how third party cookies work in the different browsers and what you should change to make it work.