Is there any SQLite Manager for MAC OS X which is able to show ER Diagram (Relationship between tables)?
You could give SQLEditor a go, check it out here. It supports using JDBC drivers for SQLite according to this page.
Admittedly, it's not free, but it does come with a 30 day trial period to determine if it's suitable for your needs.
As another option it seems that MySQL Workbench may be an option to use, as a plugin has been released supporting SQLite export read more about it here. I know from firsthand experience MySQL Workbench is reasonable to work with and it's available on OSX.
I use Visual Paradigm, there's a free version you can use :) Also has a Windows version.
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