Whats my next step to a beautiful lawn

[j-sin]

Charlotte NC lawn

Ok so we bought our home in march and the lawn was kinda sorta ok
it has existing fescue was thin in some places and a million dandelions
or whatever those small white flowers that pop up

so I did some research on here tested my soil and put down the proper amount of lime per my local soil dept suggestion. I then "waited" for labor day

once labor day hit I core aerated my lawn, went over it almost 3 times
I broadcast about 8lbs of high quality John Deere Seed and Lesco starter fertilizer from John Deere landscapes as directed.

It has been 3-4 weeks now and I want to be prepared for my next step

When do I need to start spraying for broadleaves?
What other applications are coming due

thanks so much!