btrfs definitely supports extended attributes (and if it didn't you'd get ENOTSUP not EPERM when trying to use them). It's far more likely this is because you cannot set certain xattrs within a user namespace (such as some security.* ones) -- and LXC is being used with user namespaces in ChromeOS.
In fact, I added code to Docker almost 4 years ago to ignore ENOTSUP on xattr errors specifically because of filesystem support (AUFS was the issue at the time). So if it was a support issue you wouldn't see it, because the code already handles it. :P
In fact, I added code to Docker almost 4 years ago to ignore ENOTSUP on xattr errors specifically because of filesystem support (AUFS was the issue at the time). So if it was a support issue you wouldn't see it, because the code already handles it. :P