The Kenmore Elite Trio from Sears and the LG French door refrigerators are the same units, only labelled differently for the merchants.
If at any time (even if you got it fixed for free somehow... most of us aren't finding the solution though!) you have experienced a melting light housing in your unit (due to the lights not turning off) please file a complaint with www.cpsc.gov with your information. The potential for a househouse fire or serious injury is too much of a risk.
This happened to us this weekend, Sears refused to help us since we are "out of warranty". It didn't matter that their product has a serious safety issue though. They are through with the customer once the credit card is charged. Don't use the Sears card to buy anything there either, it's like giving up all of your consumer rights!