You can buy something called 'Rootzone Mix' for topdressing lawns or for sowing lawn into. It is a mixture of screened topsoil and sand and is much easier to level than sand, is better-draining, and may have some fertiliser mixed in with it - normally delivered in one tonne bags. Also, there are seed mixes which are specifically for shady lawns. Most lawns (and plants in general) don't grow because there is an underlying problem which cannot be fixed easily. This problem is normally to do with soil quality and, most of all, because there is either compation in the soil or rubble / cement / builders' spoil only an inch or two beneath the soil. Many, many new house suffer from this, and after the build is completed the builders put a thin skim of soil over everything, bung in a lawn or some plants and disappear off into the sunset. These are the gardens that never prosper, and then only way to fix them is to excavate the whole lot and sort out the soil - I am a landscape gardener with ten years of dealing with these places! Fixing the surface of things looks great for a while, but the old problems always return.