I have figured out this issue finally.
1) Download sqlite-netFx46-setup-bundle-x86-2015-1.0.105.1 from
System.Data.SQLite: Downloads Page[
^]
2) Install it with checking "Install the designer components for Visual Studio 2015". I noticed that the x64 install don't have this option, so please always install x86 version
3) Restart vs2015, then the SQLite source appears in database conntection.