If you chose to synchronize an independent mail account in Thunderbird (whose Inbox, Sent,... folders are not shared under "Local Folders"), then you must create a mail account on the mobile with the same account name as in Thunderbird. This is the name of the mail account and is called "Account display name" in the mail account creation wizard. Note that if this name is incorrect, you'll very likely have to recreate your mail account since it is not possible to modify it after the creation.