SQLite happens to be among - the relatively few - data sources that Tableau cannot natively / directly work with. You will therefore have to use a ODBC connection with a custom configuration file, Tableau Datasource Customization (
.tdc) file. This XML text file will assist Tableau in properly connecting with your SQLite data. I have attached a template file, if it can be of help. also here is a link to how these custom connection files work. http://onlinehelp.tableau.com/current/pro/desktop/en-us/help.htm#odbc_customize.html
Let me know if it is helpful. I can otherwise guide you through the process, if you forward a workbook.
Good luck and cheers, -Birgit