How you interface to the ADO.NET APi's is really a matter of personal preference.
If you are comfortable coding using object-oriented COBOL and accessing the ADO.NET classes directly then this is certainly a viable solution.
If however, you are accustomed to using procedural COBOL with embedded SQL statements using EXEC SQL ...END EXEC or if you have existing applications that already use EXEC SQL then you might want to look at using OpenESQL with the DBMAN=ADO directive.
We have tested the DBMAN=ADO with ADO.NET providers for SQL Server, Oracle, DB2 and others but I have never tried with the SQLLite provider.
Open up the ADO.NET Connection Editor from Visual Studio IDE-->Tools-->Micro Focus COBOL and look under the providers tab.
Do you see the SQLLite Provider listed?
This OpenESQL ADO.NET support is documented here: