Problem with Lawn Weeds
We are glad you asked.
Controlling lawn weeds begins with knowing what weed you are fighting, and then moves to proper lawn management and prevention and control.
We can't tell for sure but suspect this may be a perennial grassy weed called Nimblewill that hasn't greened up yet. (It's not very noticeable in the growing season).
Take a look at the photos and information on this page from our website (click on the name to find more information:
Check out nimblewill, but also try pulling a piece of the weed in the yard. Is it attached to a long-running root/stolons above ground? Then take a look at Bermuda grass and compare.
Read through the links which will give you ideas on how to best manage your lawn to prevent weeds.
Grassy perennial weeds are the hardest ones to control. You would not be looking for fertilizer but a non-selective herbicide (in case of nimblewill), that you would use to kill those areas back completely in late summer, and then overseed.
If you've not done one lately, we'd suggest a soil test, which would tell you how to specifically improve the area, and what fertilization you may or may not need.
Here is that information: https://extension.umd.edu/hgic/topics/soil-testing