I am using Sqlite.Net in my Xamarin.Forms
application. So far it has been great at returning lists of objects if my object is a class like so:
Sq
It sounds like what you want to do is essentially recreate ADO.NET. When you say "DataSet", I'm guessing that you are talking about ADO.NET. This probably means that you don't want to use the ORM functionality built in to the SQLite.Net library.
I have created this version of the library that will allow you to do flat table reads from an SQLite database. It means that you CAN read the data in to an ADO.NET dataset if you like.
https://github.com/MelbourneDeveloper/SQLite.Net.Standard