The charger for the LG Axis is rated at 700mA. Normally, USB ports supply 500mA. In my experience, my phone (LG Axis like yours) charges VERY slowly off of a computer, or, depending on what's running, discharges. Thus I believe that my phone automatically goes into high-power mode when plugged in, and it draws around ~450-550mA (drawing the extra from the battery. Granted the 450-550 is complete BS I pulled off of the top of my head).
Thus if you kill all of the apps running on your phone, you might be able to get it to charge. Otherwise there might be high-current car chargers on the market, I don't know.
It is annoying that your phone can't be off and plugged in, though...