So basically I bought a Lava Soar cable a while back and it broke on me. They sent me a new one but I need some more cables. I figured I'd use the cable from the Lava Soar since it's like 18ft.

I'm not sure how to go about making a cable with this kind of cable though. Looks like it's two conductor and some shield.

I have tons of TS connectors laying around. How would I go about it?

If you are making a mono cable solder the shielding to the sleeve and the center to the tip, for stereo shield to sleeve other two conductors to ring and tip respectively.
according to lava's website, it has dual conductors yeah. so if you wanted to make a stereo cable you could do that. or just use one of them, and ground the other with the shielding too