Q.Specific Lawn weed control
My lawn is being taken over by a creeping weed with a small yellow flower (photos-enclosed)
I would like advice on how to treat/remove this weed without killing off my lawn.

This weed is Lesser Trefoil.
If the clumps are small and few hand weeding may be practical taking care to remove the whole plant.
In most cases where Lesser Trefoil has been allowed to spread, chemical control will be necessary to control this weed. Choose a selective weed killers that lists Trefoil. One application is usually not enough, so repeat 6 weeks later if necessary for complete control of this weed.