Is there any way I could lock up my Mail client so that only I can read my emails(which are present locally on the machine)
I would think a good way of doing this might be to package your ~/Library/Mail folder within an encrypted disk image. As long as it was allowed to grow to an acceptable size, I think it would work. You would need to move the Mail folder into the disk image, then create a link from your ~/Library folder, called Mail, to the "real" mail folder on the disk.
In order to get to your mail, (I imagine), firing up Mail.app would follow the link to the disk image, which would prompt for your password, as it needs to mount.
Once you're done with your mail, you would be able to dismount the disk image and voila.
Never having tried this, I have no idea if it would work.
This question is more or less related.
Some answer will allow you to protect the launch of Mail.app
However, like some people said on the question, it won't fully protect you, since the mail database is accessible on your file system, and it's not password protected.