Вы можете попробовать этот код
using (var location = new SQLiteConnection(@"Data Source=activeDb.db; Version=3;"))
using (var destination = new SQLiteConnection(@"Data Source=backupDb.db; Version=3;"))
{
location.Open();
destination.Open();
location.BackupDatabase(destination, "main", "main", -1, null, 0);
}