can I lock a mailbox so it is secure

- There are paid apps (has free trial) like

http://www.cisdem.com/resource/password-protect-mac-mail-app.html

- Use an encrypted disk image for the Mail app. See near to end of:

Password protecting Mail accounts

- Create new user for yourself and setup the Mail app only in that account. You will have to log into the account to use the Mail app.

What part of the email process are you intending to be secure?

Almost every eMail provider does not store email messages on their servers encrypted, and most do not transport your messages across the Internet encrypted. Keeping them locked up once they get to your computer and under your control is almost laughable.

If you have sensitive information, having it anywhere near the Internet in any fashion leaves it trivially close to being Public.