You can fry them, they're pretty good.

Weeds are opportunistic. They're outcompeting the grass because that environment is not good for the grass (for whatever reason), but is apparently good for the weeds.

Seed the lawn with native mixes for your region, maybe fertilize, and then maybe the new grass will outcompete the weeds.

Personally, IDC about lawns and let whatever grow. If "weeds" can outcompete the grass, then that's fine by me. Green is better than brown or dirt.

Make the grass healthier - mow at the height for the species and overseed again when appropriate for the species. That will help crowd out weeds.

Ignore the weeds, or keep pulling them out. July is not a good time to address lawn health; pesticides rely on actively growing weeds to work.

If it's acceptable for your situation, just let them be, and there will be fewer next year.

When a specific weed becomes invasive in an lawn it's because there is an imbalance in the soil. The more you fight, the more you keep the imbalance, which favors the unwanted weed for the following years. Let it proliferate this year and you will recreate a natural balance in which no species dominates.

Mowing several times a week and keeping the grass short helps against most weeds. Mowing stimulates the grass to spread out / grow horizontally. On the other hand, your grass isn’t growing a lot now; as the heat has turned it yellow but you should still mow to keep the weed in check. I’m following a different approach myself: I have replaced most of the lawn with flowers that are suited for insects; lawns are useless from an ecological viewpoint - but that wasn’t your question.

Those look like narrow leaf plantains

I've never tried to remove them, so I'm not sure what the ideal way to deal with them would be

There is some good advice here on dealing with this particular plant. Assuming it's not native for you, that's worth pursuing.

I'm going to be that annoying person and suggest this is a good opportunity to rethink the concept of a lawn. A lawn forever requires a lot of maintenance because it's usually a monoculture and usually non-native. Allowing that space to become a habitat for a variety of useful native species is very rewarding. You will need a reliable way to identify plants (like an app) to determine what's good to keep or remove. It will require a lot of maintenance initially, but a robust native ecology once established will require less attention with time. Your local fauna will thank you.

I'm fairly certain that is plantain, but I'm not sure which species. Cornell has a good breakdown of species and how to deal with them towards the bottom

Something is killing the grass in that picture. You need to figure out what it is. Common issues include fungal infections, insect damage or soil nutrient inbalance issues.

Dig around and see if you can figure out what is cause the grass to die. If it's an insect, identifying the insect can help you figure out how to control it. If it's a fungus, planting resistant species/varieties can eliminate the issue. For the soil nutrients sending a sample into a soil lab is relatively cheap and gives you an idea of what might be wrong.

The weed is buckhorn plantain. It's a perrenials that you have to remove the entirety of its roots (almost impossible). It's relatively easy to kill with a well timed application of 2-4D.

https://turf.purdue.edu/buckhorn-plantain/

It does produce a massive amounts of seeds that can remain dormant for decades. So it will likely keep popping up for quite a few years.