It looks like a geranium (cranesbill) to me, clearly self seeded so you must know the mother plant. I would take a guess at endressi which is a peachy pink, flowers from April/May until late autumn.
Personally I always feel it is better to go with nature. That part of your garden doesn't want to be lawn so don't force the issue.
As the geranium likes it there you can encourage it by removing the dandelions, lamium, and anything else growing amongst it then splitting the geraniums and planting evenly all over. It will root quickly if you water it and by summer you will have a sea of pink flowers which is excellent at suppressing weeds.
Wildflower meadow is another option but Labour intensive to be kept pretty. For large parts of the year is will simply look abandoned and neglected.