While we wait for someone who knows more about Lamarckism than I do to extract a self from it, I'll have a go myself.
Lamarck saw evolution involving two separate processes. One was "complexifying," the generation of new features and capabilities by a faculty that he referred to as "a subtle fluid" located in the bodies of living creatures. The other process was the harnessing of such novel features, through use and disuse, to adapting creatures more closely to their environments. "Complexifying" generated variation, use and disuse winnowed it and shaped it to improve the fit between a creature and its environment. Superficially, complexifying resembles mutation in generating variation, use and disuse resemble natural selection in how they relate to variation.
Use and disuse were something the creature itself did. By applying aspects of new features to life's problems the creature could reinforce those aspects, either by developing a new habit or by reinforcing the tissues involved, as a giraffe by stretching further its already long neck could make it longer still. Both habits and enhanced tissues would be inherited by the creature's progeny.
Again, if we assume that creatures like us are bound to identify with the obvious success of evolution and wish to participate in its progress, our opportunity to do so can come only through use and disuse. Lamarck made it clear we individually have no access to whatever is responsible for "complexifying. "
Use and disuse have a wonderfull puritan quality to them. We are to dutifully exercise those talents and tissues that make for success, while shunning those that are not useful but merely pleasurable. Heaven forbid that through entertaining such fruitless pleasures we build them into future generations. So Lamarckism lays heavy obligations onto the individual: to exercise those talents and tissues that are useful, to shun those that are frivolous, and to appreciate the difference.
Lamarck's specialty was invertebrates. He didn't have to worry about his theory turning them into puritans. It may not even have occurred to him that, taken to its logical conclusion, his theory could turn them into Calvinists! But that, or something like that, is implied by some of us bearing within us the faculty of "complexifying, and some of us not. That, and that alone, is what carries evolution forward, that is the only significant contribution one could make to the progress of evolution. Use and disuse are merely lateral movements adapting creatures to this or that environment. But Lamarck presents complexifying as a gift from the gods: we either have it and are blest, or we don't and our lives are blighted.
Lamarck's theory has been discounted because today's science knows of no mechanism by which attributes acquired during life can be passed on to progeny. As far as the self implied by Lamarckism goes, though, I think the natural world bears it out fairly well. The birds and the bees all seem busy developing their talents and adapting to their environments. It seems inadequate in only one instance: us. We clearly all have a creative faculty, we each possess the ability to complexify. Which means that faculty is no longer an inscrutable "subtle fluid" but something we should be able to identify in ourselves. And once we do we'll know what it is that drives all of evolution.