Hacienda La Lucia was established in 1852 by Gustavo Dausó (apparently an adaptation of the French Dausau), a French immigrant from Nantes and his wife Clementina Dorion, named in honor of his daughter Lucía Dausó Dorion (1839-1909).  It was inherited by Lucía and her husband and also Frenchman Luis Lavergne. 
Approximately 50 cuerdas of Hacienda Lucia were foreclosed upon in 1881 by Julian Leroy as the result of a court claim for unpaid debt against Luis Lavergne.  The November 19, 1885 edition of La Gaceta de Puero Rico  reports that as a result of a court case established by José Facundo Cintrón against Lucia Dausó de Lavergne, the judge ordered the sale in public auction of the 330 cuerdas Hacienda Lucía and all its structures.  The licitation resulted in its acquisition by Cintrón for the amount of 82,035 pesos.  Cintrón was also owner of Ingenio Laura of which you can read on the PR Trapiches Project page.
Its machinery photographed below was installed ca. 1883.  In 1893 it was damaged by Hurricane San Roque, we do not know if that is when it ceased operating as a trapiche but reportedly sugarcane was grown on its lands until the 1930s and after it ceased grindinging, its sugarcane was sent to Central Roig  for processing.
In May, 2014 the Municipal Government of Yabucoa was granted permission to develop and maintain this property as a tourist attraction highlighting the importance of the hacienda in Yabucoa's rich sugar industry history.  During our visit in November, 2014 we saw no work being done on this regard.