Sorry, but your code is a disaster. Nevermind using SQLite, you clearly don't know how to code.
You're getting a null reference exception because
Klienci
is not instantiated. It's only instantiated inside this loop:
Klienci = new Klient[tabelaK.Rows.Count];
so if there are no rows, Klienci will be null.
Of course, you're instantiating for every single record, it should be instantiated outside of the loop, so you're never going to get the data into an array anyways.
And why would you want it in an array?
This:
string elo = Convert.ToString(sthnk.Klienci.Length);
MessageBox.Show(elo);
is sort of a disaster too. You could just do:
MessageBox.Show(sthnk.Klienci.Length.ToString());
or:
MessageBox.Show(String.Format("Length = {0}", n));
So, sorry to say, it's not SQLite that is the problem, it's your code.