I would core aerate now and allow the plugs to disintegrate. September I would mow my lawn down short so the grass won't be shading the seed. Short as in 2". Top dress with 1/2" of topsoil, not compost. There are topsoils with compost added. But a word of warning; you have no idea what is in that compost. I've run into topsoil with added compost where I couldn't get a petunia to grow. Pesticide residue from homeowner 'clean green'...I would stick with screened plain old topsoil.
Dump piles all over your lawn and then start spreading with rock rakes or grading rakes. This next step is the part you cant miss! You need to rent a roller (fill with water) to compact, regrade and compact again. Then seed, rake lightly with the tines of a leaf rake upside down and roll again.
Keep moist. Shallow watering. In less than two weeks you should be able to do the virgin mow at 3.5, bag clippings. Fertilize with a low nitrogen formula. Dr. Earth I think has a fall fertilizer and if you haven't tried one of these 'organic' lawn fertilizers you simply must with all the work you are putting into your lawn. Costs more but you need fewer applications and WOW. I know these dang lawns and trust me, to be wowed with a product for lawns is RARE.
Make sure you use a rotary spreader for seed and fertilizer. Drop spreaders are awful. Throwing by hand is a big no no.
For lime, you must do a pH test first. If it reads below 6.5, lime according to directions right after the first rough spreading of the topsoil. Remember you've got two soils to test; the original bed and the topsoil. Do you live with a lot of rainfall? Then grade and grade and roll and roll and grade again.
Get the best seed you can find. I always used 'Professional's Choice'. That was for the Pacific Northwest. ZERO weed seed. This means some thought and care went into producing that seed and the germination rate is the highest. Don't use seed for shade. Unless you've got some shady areas use it just for those areas mixed into the seed you've used for the entire lawn. I hope this helps! Here is one of my lawns rehabilitated shortly after construction of that walk, brick wall and screens...
Here is a tip on spreading mulch or topsoil or rock; spread the pile to the depth you want do not thin out in an effort to cover more area. When you have done this then you go back and dump more soil or shovel out of the wheel barrow to cover the obvious areas that haven't been covered with soil. This ensures an even coat of soil, the depth you want and when you grade and roll you will get a more even surface.