I'm hoping someone is reading this who knows more than me about sqlite and Python (which isn't difficult seeing as I've never used either), but my rather generic suggesion would be...
As you appear to already have a working project written in VB.net which uses sqlite, take a copy of it (I'd copy the entire solution folder, .sln file, project, code files and all, just in case anything you do in SharpDevelop breaks it, it probably won't but there's no harm in erring on the side of caution), and then open the copy of the solution file in SharpDevelop (it should be able to open Visual Studio solutions).
Are you able to open the solution file? Does SharpDevelop report any errors when opening the solution file? Are all the projects in the solution showing in the solution explorer? Does it build? Does it do what you're expecting when you run it? Can you debug it and do the things you'd normally be able to do in a debugger?
Doing this will tell us whether SharpDevelop is playing nicely with sqlite.
If all the above works, then the problem is probably with Python or SharpDevelop or how the two interact with each other. So I'd suggest building a Python project from the ground up, i.e start with a "hello world" project and check whether it builds and runs and whether you can debug it, and gradually add to it until you find that either your app can happily talk to sqlite databases or until you find the feature that doesn't work.
Sorry, this is a rather generic and uninformed reply, but I hope it's better than no reply at all :-)
Simon