what then happens to the lactic acid when sufficient O2 becomes available again (and the burning sensation disappears). The C+ article suggests that when the LA is further oxidised (burnt) it yields the rest of it's energy and that energy is available to do useful work
More or less. The initial part of glucose metabolism (glycolysis) yields 2 molecules of pyruvate and 2 of ATP (adenosine triphosphate, a cellular energy carrier). The pyruvate is then fed into the citric acid (Kreb's) cycle and electron transport chain which breaks it down further to yield yet more ATP. (I can't remember exactly how much but I'm pretty sure it's more than another 2 molecules).
In the absence of oxygen, the Kreb's cycle won't work and pyruvate stacks up which would stop further glycolysis. The pyruvate is therefore converted to lactate. This yields no further energy but it removes the pyruvate 'block' and regenerates NAD (nicotinamide-adenine dinucleotide, a hydrogen ion carrier) allowing glycolysis to continue.
When oxygen is restored, the lactate is re-converted to pyruvate which then continues on its way through the aerobic pathways.
Although glycolysis releases very little of the energy content of glucose it can release energy faster than the full oxidative pathway at the expense of a lactate build up, hence the reason why you can only sprint for a short period.