I have used nuget to install
Unable to load DLL 'sqlite3': The specified module could not be found. (Exception from HRESULT: 0x8007007E)
db = new SQLiteConnection("Data Source=C:\\Users\\xxxxxxx\\Desktop\\mydb.sqlite;Version=3;");
I think it could be an architecture mismatch between your application and the sqlite driver.
Download a precompiled binary package matching your architecture here http://sqlite.org/download.html and place the .dll into the bin\Debug or bin\Release folder. I think it could probably be an architecture mismatch between x86 and x64.
From documentation you can see the needed deployment structure:
<bin>\App.exe (optional, managed-only application executable assembly) <bin>\App.dll (optional, managed-only application library assembly) <bin>\System.Data.SQLite.dll (required, managed-only core assembly) <bin>\System.Data.SQLite.Linq.dll (optional, managed-only LINQ assembly) <bin>\System.Data.SQLite.EF6.dll (optional, managed-only EF6 assembly) <bin>\x86\SQLite.Interop.dll (required, x86 native interop assembly) <bin>\x64\SQLite.Interop.dll (required, x64 native interop assembly)