Look more like a slug
I really don't know why but their are a fair few but it dose look like slugs no legs
I think your lawn looks quite healthy. That looks like a slug and I don't think it will damage your lawn. I don't see the brown bit you state on the title.
The patch of broad leaf grass is probably a bit of meadow grass, Poa Annua. You can dig that out and re-seed the area if it's an eye-sore.
That's a better pic
The new picture is still looking healthy considering at this time of year with a very hot and dry spell. Any slightly brownish patches will be drying grass. Make sure you scrake/scarify your grass before cutting. This will lift the thatch that's dead and blocking water from entering gaps. Do this a few times and then mow the lawn to see. You could top dress after that to fill in any hollows.
It's soaking in the UK but I will rake it before cutting that I usually do but not top dressed before
I just want to add, if your lawn has been excessively wet, sometimes the grass can develope a brownish tone which will fade once the soil underneath starts to dry up. Only top-dress when you have really raked up the lawn very well or it will be a wasted task.
Same here ?