Ouch I think I been there before, I think probably the problem is your MFE_HOST is not a subdomain of LMS_HOST but in order for my theory to be true it shouldn’t work at all not that sometimes it do or sometimes its not.
To resolve the issue for me when I had, I changed the cookie domain for use case make sure the cookie domain is “. domainexample.click.” I think that value is lms.env.yml it should be SESSION_COOKIE_DOMAIN: ". domainexample.click." Assuming MFE_HOST is not subdomain of LMS