LETS are to economics what homeopathy is to modern medicine. They have some appeal among those who feel mankind has being going backwards since the discovery of agriculture but any justification for LETS collapses when subjected to the tiniest amount of rational analysis and/or when real world experience is taken into account.
They suffer obvious and deliberate flaws in terms of providing a medium of exchange or a unit of account - both vital properties of any money. And without the backing of a sovereign government, I certainly wouldn't trust one as a medium or long term store of value (LETS collapse all the time).