I found that that MATLAB has JDBC drivers just for SQLite. These drivers do not expect a client/server database. They work fine with the flat database file SQLite produces.
There are also MEX clients for SQLite. These client would be more difficult to include in a standalone compiled MATLAB program than a JAR file. So I will concentrate on how to use the JDBC drivers.
First things to do is to get that special JDBC driver for SQLite for your platform. There are many different drivers for this purpose.