Questions:  Does the limestone base extend out beyond the cement edge? If yes, how far?  How deep is the soil above the limestone base?  Do you salt the cement in the winter to melt snow & ice?  Do vehicles occasionally drive off the cement onto the lawn?  Is the problem on one side of the drive or both sides?  Is the problem area a high foot traffic area?  Does the problem exist all growing season or only when?
Unfortunately the photos confirm you have a problem but don't provide enough detail to determine what the cause is.  I suggest you do a soil test for the problem area(s) to learn more about your soil including soil type, pH, nutrient levels and more. Knowing the type and fertility of your soil is the starting point to establishing & maintaining a strong turf that can resist diseases, moss and insects/grubs and look great. More info here: Don't Guess-Soil Test-MSU and MSU Home Soil Test-self mailer  Tell them this is a problem area next to the concrete drive installed in 2020.  Knowing the soil status we can treat the area to create a favorable turf environment.  When you get your soil test results email me back with the access code and we'll go from there.