Note: in Internet mail messages, the addr-spec in a Content-ID
[MIME] or Message-ID  header are enclosed in angle brackets
Whether this is neccesary depends on the mail client. Gmail requires the angle brackets, Outlook does not.
To make this work in the above example this should be used instead:
Type => 'image/gif',
Id => '<ltrhead.gif>',
Path => 'fake_letterhead.gif',
The current version of MIME::Lite
(3.0.1) does not add the angle brackets, but that could change in the future so be sure to check the documentation.