(connect to /var/imap/socket/lmtp[/var/imap/socket/lmtp]: Permission denied)
The file system permissions of your socket file /var/imap/socket/lmtp(*) are set in a way so that the postfix process (running under user "postfix") just can't write to it.
Pascal
(*) The name and location of the socket is defined in your cyrus.conf, lmtpd(8) via unix socket transport.
