Well, an acre is 43,560 sq. ft., so if you have about 21,780 sq. ft. of lawn (slighly less because I didn't take out for the house and garden or whatever else isn't lawn). Say you have 20,000 sq.ft....you are only putting on 1/2 of the recommended rate of lime. I would recommend putting down at least 20 bags this spring and then try seeding again in the fall. If your pH isn't optimum, you're not going to be happy with the results. You shouldn't expect to see results from the lime within the next 6 months...it takes about 6 mos. or a year to see results.
It is really better to seed in the fall....MD's springs are too short to give the grass a chance to establish roots before it gets slammed with hot weather and possible drought conditions. You can seed in spring if you're really good about watering it (best to water it in the early morning...and give it a good deep watering so the grass establishes deep roots). Seeding in the fall is still best though....I would seed between August 10th and September 10th...make sure to water at first if it is a dry summer.
Try seeding with creeping red fescue. It is a shade loving grass...if your lawn is too shady for that, then you might as well mulch it all.
Good luck!