Why don't your lists accept my Google Mails properly?
When Google sends email, it sends it with a "Sender" of "<user>@gmail.com" (or whichever domain you're registered in). Changing your From address does NOTHING to change the Sender header (and envelope header) that Google Mail sends.
EZMLM checks the envelope and Sender header. These all need to match up to your subscribed address or your email will be rejected.
This is not a bug.
Complain to Google. You are effectively sending email as <user>@gmail.com while you subscribed with firstname.lastname@example.org (for example).