<font color="blue"> As far as i know, you cannot go too heavy with lime </font>
Get a soil test. Costs $5-$15. Check your local ext school or LESCO. Get the "deluxe" test. It will tell you how much Phosporus (P) & Potassium (K). you need in addition to the lime which adjusts the pH (Acid-Base).
Step 1 is getting the soil chemistry right (see above).
Step 2 depends on how aggresive you want to be. If you feel it is best to start with a clean slate, spray roundup to kill grass & then till it under. At this point you can add soil ammendments if desired/needed. Keep in mind, compost ain't dirt cheap! I paid $25/yard in MA. Then you can seed, hydroseed or sod.
A less aggresive tactic is the above mentioned aeration / overseeding. Do not use any selective weed killers (weed & feed, halts etc.) the new grass doesn't stand up well to them. Water, Water, Water!.
If you plant in the spring, you will need to water all summer long. The best time is to plant in the fall (labor day +/-). Less weed seeds floating in the air and the grass has a chance to grow the roots deeper before the summer droughts hit.
It takes a couple months for the lime to adjust the pH of the soil, so if you do that now, a less aggresive aeration, and fertlize the lawn (see links for recommendations on how much, 2-4 lbs actual N per 1,000sq feet depending on grass variety). You may be pleasantly surprised at how the grass comes back. If it doesn't your chemistry is all set for you to aerate & overseed in the fall.
Spend some time on the web
My favorite lawn sites
Cornell
lawn talk
bud seed
The first two are for cool season grasses (not sure where you are). use google to find your local college info.