Sorry but it's really hard to see any details in the picture. You could look at images of Ajuga and see if that fits.

Thanks floral_UK.

I attached more pictures. Can you please confirm that the weed is Ajuga indeed?

What is the best way to kill it outside of pulling.

Yes it's Ajuga reptans. I don't deal with weeds much and when I do I pull them. In cultivated beds I use pulling, hoeing and mulch. I don't have a lawn. If you want to use a herbicide you'd need to research one which kills broad leaves weeds and not grasses. But I'm afraid I have no expertise in weedkillers.

You are lucky, m k. I tried to naturalize Ajuga in my lawn, because it supports many beautiful butterflies https://en.wikipedia.org/wiki/Ajuga_reptans#Uses, but it looks like the plant doesn't like my soil or my climate, or may be both ;-)