The problem is that your digitizer is broken. It is repairable. I've done this repair for two different customers. The charge for the repair will completely depend on who you take the unit to. I do not think that the manufacturer warranty will cover it, but if you are paying for insurance, physical damage should be covered. It completely depends on what kind of insurance you have on the device. Hopefully your insurance will cover this incident. If not, seek a local repair shop and get a quote. I'm not sure where you're located, but you can email me for a quote as well at firstname.lastname@example.org. Good luck!
There are several models of the Optimus G. I have been able to find replacement components on Amazon.com by searching for "LG Optimus G digitizer LCD" which brings up several purchase options for either the LCD by itself, the digitizer by itself or both of them together.