Hacienda La Lucia was established in 1852 by Gustavo Dausó (apparently an adapatation of the French Dausau), a French immigrant from Nantes, apparently named in honor of his daughter.  It was later owned by also Frenchman Luis Lavergne who was married to Lucia Dausó Dorion (1839-1909), the daughter of Gustavo Dausó and his wife Clementina. 
Its machinery photographed below was installed ca. 1883.  In 1886 while under the ownership of Luis, the 330 acres Hacienda Lucia was acquired by Jose Facundo Cintrón for 82,035 pesos due to an unpaid debt.  Cintrón was also owner of Ingenio Laura of which you can read on the PR Trapiches Project page.
In 1893 it was damaged by hurrican 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.