This weed looks like Japanese Stiltgrass, though additional pictures of it growing in the lawn may be more conclusive. If so, the herbicide you used is not intended to control it, as it is only labeled for broadleaf weeds. (Broadleaf weeds are not grasses, despite some grasses having a relatively broad leaf blades compared with others.)
https://extension.umd.edu/resource/weed-identification-photos

Since Japanese Stiltgrass is an annual (meaning it only lives for one year, and in this case, dies in winter), that means it must return from seed each year. While their seeds can unfortunately remain viable in soil for many years, it also easily moves into new areas on the leg fur or hooves of wandering deer. Keeping deer out is the main tactic to control rampant Stiltgrass spread, since existing seed banks can otherwise be treated with preemergent herbicides each spring until depleted. If you are not able to fence-off the entire lawn area, treating for Stiltgrass may a persistent long-term problem since it is so aggressive and invasive. Here is more detailed information on Stiltgrass management: https://extension.umd.edu/resource/japanese-stiltgrass

If your weed does not appear to be this grass, please send additional photos so we can try to ID it. In areas of lawn that tend to have persistent weed problems, this indicates conditions are not suitable for good turf growth, since healthy lawn tends to out-compete most weed seedlings trying to establish. A laboratory soil test may be of use in case nutrient levels or pH needs addressing, but any areas receiving too much water (or poor drainage) and not in full sun (6-8 or more hours) will continue to struggle. In that case, they are best re-planted with turf alternatives better suited to those conditions. There's a lot of good information on general lawn care and troubleshooting on multiple webpages, accessible from this list: https://extension.umd.edu/resources/yard-garden/lawns/lawn-care-and-maintenance

Miri

You're welcome.

Thank you for the photo - it does appear that this is Stiltgrass, as this is how it tends to look when kept shorter than normal via mowing.

The overall browning of the lawn could be in part due to typical summer conditions (as Fescue and other cool-season turfgrasses go semi-dormant in summer to tolerate the heat and drier weather) and/or the fairly ubiquitous diseases that outbreak some summers, such as Brown Patch. Going through soil testing and then overseeding with good-quality seed this autumn should help thicken-up the lawn for next year if no other issues are present. Consider core-aerating the lawn prior to seeding as well, as this improves drainage and oxygenation of the root zone, plus seed-to-soil contact to improve germination.

Miri