As far as I could understand your setup, you need to install an additional pair of wires between phone company's demarcation point (the gray box outside on one of your walls) and the main outlet (kitchen, I assume). Then that additional pair will have to be spliced (connected) to the pair of wires, red and green, leaving to the living room.
The additional pair of wires may already be pulled somewhere inside your house. If that's the case, you'd need to find where it goes to, and then pull a cable between that point and the living room jack or kitchen.
If there is only one pair entering your house, then you'd definitely need to call a phone tech to install it. Well, I mean, you need to call the phone company and have them come out anyway, it's just that they would not charge you if they only drop the second phone line at their demarcation device. If they have to work inside your house, then they'll charge you extra. And, again, to pull the extra pair between their box and one of your outlets, you still need them because they would need to open their box for the connections.
The other suggestion: call them to drop the line. When the tech shows up, let him do his work, and as he opens the box, ask him how many pairs are entering the house. If he says two (or more), find the hole on the wall behind the demarc box and follow the cable to find where it lands.
Dmitri Abaimov, RCDD