Running "make initialize-database" will create the database file owned by whatever user is running make. This is probably not going to be the user that will be accessing it from the web interface. It should be read/writable by that user. The directory containing the database file should also be read/writable by that user so that SQLite temporary journal files can be written (it seems).
To use SQLite, in RT_SiteConfig.pm:
- Set($DatabaseType , 'SQLite');