i'd suggest a soil test before adding lime. you may not need it. its primary function is to raise the PH of the soil. anything in the 6. to 7.5 range is fine for turfgrasses. some like a little more or less than others but in that range just about anything will grow. i wouldnt want fresh lime down the same time i planted seed. as far as doing a core aeration... throw the seed out and do a pass in each direction with the aerating machine. (assuming this is just an overseeding and not a full blown lawn rennovation)

if you do need lime, or pelletized sulphur if your soil is alkaline, i suggest waiting till it starts going dormant in the fall. give the stuff all winter to get watered down into the soil and reap the benefits next growing season.