Thunderbird: Sync NON gmail address with Android?

[joelshort]

I'm using a non-gmail email address that is tied to my hobby/business website. I use Thunderbird as my email client. Is it possible to sync my desktop thunderbird with my android phone, WITHOUT using a gmail email address?

Ex. my email is joel@mydomain.com and I use Thunderbird. I'd like to sync joel@mydomain.com messages with my android phone.

Thanks in advance.