iPod classic 80GB won't charge from usb power adapter
I looked into the amount of current available from a USB charger when investigating how to charge multiple iPhones / iPads simultaneously.  Below is something I learnt that might be relevant.

There are several different ways that a charger can "tell" an iPod how much current it can provide - the iPod can't determine this directly.  If the charger is a computer, it will communicate this through a data transfer (similar to transferring MP3 file data).

But a simple charger won't use this method.  Instead, there are various standards (some proprietary, I believe!) which specify how much current can be provided, by providing certain voltages at the data lines.  USB has four pins: one ground, one power, and two data.  For example, apparently 2.8V on one of the data pins and 2.0V on another means "you can draw up to 1 amp".  See this link for some detail, although I think some of that is out-dated.

I'd guess that the LG adaptor doesn't provide the signalling that the iPod expects.  I don't know a way to resolve this, other than to try a different adaptor - sorry.