The next hurdle in my Windows Azure project was the missing support for Sqlite. I needed to add these lines to the configuration to get it:

<system.data>
 <DbProviderFactories>
  <remove invariant = "System.Data.SQLite" />
  <add name         = "SQLite Data Provider"
       invariant    = "System.Data.SQLite"
       description  = ".Net Framework Data Provider for SQLite"
       type         = "System.Data.SQLite.SQLiteFactory, System.Data.SQLite, Version=1.0.65.0, Culture=neutral, PublicKeyToken=db937bc2d44ff139" />
 </DbProviderFactories>
</system.data>

But what about the type? Azure needs the fullname. I used reflector to get it. http://reflector.red-gate.com/download.aspx 
Note: Azure needs the x64 assembly, so package it for deployment.