All that can presently (November 2015) be gleaned about by internet searching is that William R. Lawrence is the one-off composer of Fig Leaf Rag (1909) published by William R. Lawrence, New York, USA.
Surfers are welcome to contribute information about this composer.
This list is arranged in chronological order and contains 1 work by William R. Lawrence.
It does not claim to be complete and represents only the number of items located.