MOST LCC's are no more profitable than conventional airlines. In fact, most fail within a few years after they are launched. Many others just squeek by from year to year or until they finally die. Vanguard and National come to mind. Some have as wierd and twisted, Chapeter 11 filled histories as the majors - America West comes to mind here.
The reason that LCC's have a reputation for profitability is that the only consistantly profitable, reasonably sized airlines in the US (and increasingly, Europe as well) are LCC's. Regional operators used to be able to make consistant profits as well, but now even this is in doubt. Only some of the best LCC's seem to be able to consistantly make a profit, or at least come close to doing so.
SHORT......Most LCC's are NOT consistantly profitable. But those airlines that are consistantly profitable tend to be LCC's. That is the source of their reputation.