Unable to determine the provider name for provider factory of type 'System.Data.SQLite.SQLiteFactory'. with the Nuget package version 1.0.94.1
Add one more provider
<provider invariantName="System.Data.SQLite" type="System.Data.SQLite.EF6.SQLiteProviderServices, System.Data.SQLite.EF6" />
move
<add name="SQLite Data Provider" invariant="System.Data.SQLite" description=".NET Framework Data Provider for SQLite" type="System.Data.SQLite.SQLiteFactory, System.Data.SQLite" />
bellow
<remove invariant="System.Data.SQLite" />
and change the provider name to providerName="System.Data.SQLite in your connection string.
EDIT:See also http://system.data.sqlite.org/index.html/tktview/2be4298631c01be99475
What worked for me was to follow the comment on 2015-04-29 08:33:33 in the SQLite ticket:
If you switch project target platform from 4.5.1 to 4 and reinstall nuget package you will have it all working(even if you later return it back to 4.5.1)"
Might have a similar effect on config to Mihail's answer, not sure.