Looks like one of the speedwells. Its hard to be sure which from the photo but most of them stop flowering in the summer and disappear. They are annuals but seed freely. I wouldn't worry about killing it but if you really want to any lawn weedkiller will do the trick - but it will have already seeded the lawn for next year and the weedkiller won't affect that..

If you mow the lawn on a medium cut more regularly it should largely deal with the problem as it will cut the flower heads off before they can seed. (I think they look quite pretty but that's just me...)

Thanks for info, yes I think it's quite pretty too was just worried it may weaken the lawn, so with that advice I'm going to leave it there and enjoy.... Trying this year not to cut lawn too short (I usually tend to!) and more often which is not a problem as I'm happiest in the garden, thanks again?

We find the next lowest cut is fine at this time of year when the grass is growing strongly. We never use the lowest one.
This is short enough to decapitate weeds but not short enough to weaken the grass.