I’m not really sure what this weed is, there are a number of possibilities. I have the following in mind:
Birdsfoot-trefoil (Lotus corniculatus)
Horse-shoe Vetch (Hippocrepsis comosa)
Black Medick (Medicago lupulina)
Whichever weed it is, if you have not noticed it before, it’s arrival in your lawn probably has something to do with the drought conditions. A number of lawn weeds become a lot more prominent in dry weather. If you don’t water your lawn in dry weather the grass will not grow as strongly or possibly not at all. Meanwhile certain lawn weeds take the opportunity to thrive in such conditions; they are like vultures hovering over a carcass at the start of a dry spell.
If I were you I would live with this weed and the moss until the end of summer. The grass is tired and stressed, let it rest until then. When autumn comes, the turf can be fed and scarified, raking the yellow weed out. If you don’t mind using herbicides a general-purpose lawn weedkiller could be use to kill the weeds before raking. But simply feeding the lawn regularly during the growing season, when and if rain is forecast should deal with the yellow flowered weed. Healthy, well fed, scarified and watered grass will smother such weeds.