So in order to prevent myself from spending more money on the bag, I figured I would first reline it myself. I had already tried to clean the bag with nailpolish remover (which was a bad idea because it made the lining come off). I didn't want to try the talcum powder solution because I wouldn't want my stuff to be covered in talcum powder residue. So a new lining it was. I bought myself some cloth at a local store and went ahead with it. You can see the results here:
It came out pretty good to me. I can now use the bag without my hands (and stuff) getting sticky and it looks a lot better too. If I still like the bag as much as I do now a little while later, I think I will get it relined by LV. But as I said, I'm happy for now!