Creeping Buttercup (RANUNCULUS repens), is a broadleaf perennial that reproduces by
seed and by rooting at the nodes of creeping stems.
This is from the Western Garden Book:
It will be a lot of work if you don't want to use chemicals. In lawns, dig up creeping buttercup, roots and all or cut the tops of the
plant repeatedly until the roots stop resprouting. Improve drainage. Creeping buttercupm likes moist soil and will perpetually flourish. If improving drainage is not possible, consider planting a ground cover that is tolerant of damp soils instead of trying to grow lawn grass.( a little bit harsh don't you think?)