I will be travelling from Vilnius to Istanbul, and from Istanbul to Ljubljana. It is a connected flight with Turkish Airlines. Can I fly with only my ID? I do not have a passport.
Yes, you are allowed to transit in Istanbul without leaving the transit area, as long as you can enter Slovenia (which you can).
However, many check-in agents are not aware of this, because of how poorly Timatic, the database used by them, has described this in the past. After I discussed this with my IATA contact, the database was slightly modified.
It now says (for Turkey):
TWOV (Transit Without Visa): - Passengers with a confirmed onward ticket for a flight to a third country within 24 hours. They must stay in the international transit area of the airport and have documents required for the next destination.
Even so, although you can fly, I would strongly recommend you to e-mail Baltic Ground Services (the check-in company responsible for Turkish Airlines in Vilnius) at email@example.com, firstname.lastname@example.org and email@example.com (yes, send to all three), and ask if they know this.
Ask if they are aware that, to transit at Istanbul without leaving the transit area, you do not need documents required to enter Turkey, only to enter Slovenia, and tell them that you're travelling to Slovenia on your Lithuanian ID.
If they say you can't fly, insist that they check with Turkish Airlines (they can contact a special department)