(I'm assuming you're wanting lumber gathering closer to what warcraft 2 had)
Not exactly what you asked for, but you could give trees health equal to the number of hits required for full lumber. This will obviously have different effects than what you want if multiple harvesters are chopping the same tree, or the harvester switches trees before getting full lumber.
Another close-but-not-quite idea would be using the human lumber gathering, giving them an absurdly large lumber carrying capacity, and whenever a tree dies with a peasant nearby, one is randomly chosen and ordered to return gathered resources. They'll return variable amounts of lumber but it will look like they return every time they finish chopping a tree.