Here you go!!

  <system.data>
    <dbproviderfactories>
      <add name="SqlClient Data Provider" invariant="System.Data.SqlClient" description=".Net Framework Data Provider for SqlServer" type="System.Data.SqlClient.SqlClientFactory, System.Data, Version=2.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089"> 
    </add></dbproviderfactories>
  </system.data>
  <connectionstrings>
    <add name="SessionDatabase" providername="System.Data.SqlClient" connectionstring="Persist Security Info=False; uid=<MSSQL USERNAME>; pwd=<MSSQL PASSWORD>; Data Source=<FQDN OR IP OF SERVER>; Initial Catalog=secureconnect; "> 
  </add></connectionstrings>

They support only MSSQL - but it's not a complete implementation. 

I am very surprised as well that this has yet to be implemented. SQLite is just that lite. "SQLite emphasizes economy, efficiency, reliability, independence, and simplicity" to quote directly from the product page. It is not meant to scale to large data. Large data is meant for a RDBMS (relational database management system) that can reindex, defrag, etc.
Can SQLite do everything I have mentioned - sure and depending on memory (RAM) constraints, it can either do it well or as many have seen, crash hard. I would suggest that they makes this change. Otherwise there are always other RATs in the world (non-viral).

This is a definite need - we use 5.6 right now on a MSSQL server and it handles A LOT better than SQLite could ever do!