You can exclude your SQLite database file from being compiled to the EXE (in File Manager, double-click on it and choose to exclude it). Then, just place your SQLIte file into the “Data” subfolder of the folder where your EXE lies, and the SQLite extension will be able to connect to it if you pass DOCUMENT_ROOT as folder.
Note that we have a working sample in the Chromium demo that ships with ExeOutput. The full source code is included.