One of the apparent paradoxes of life is that we often have more energy when we're busy than when we're not. Maybe it's just that we don't have time to realize that we're tired.
But maybe it's great upward spiral of mood that we mount when we begin to engage in productive behaviors.
If we work on something productive, even though it takes energy, we also gain the emotional energy that comes from a sense of accomplishment.
Humans are not machines and the emotional aspect of our makeup contributes to behaviors that do suit purely mechanistic models. It seems logical that if we feel tired, then expending energy would make us more tired, but this is not the case.
Obviously there's a point at which we need to rest, but if we're fighting lethargy, it's often the case that taking action, energetic action, will get you moving.