Enrique enjoyed a comfortable childhood among his 6 siblings, they belonged to the Chilean upper class of Santiago; his father Luis Alfredo Lynch Solo de Zaldívar was a military attache and career diplomat, and his mother Julia del Solar Cañas was an elegant lady from a prosperous Chilean family.
In his personal life, Enrique had 2 marriage engagements: first with the young Argentine art student Romualda Barrios the daughter of a winemaker from La Rioja, they had one son Nicolás, their union did not last long and ended once Enrique moved to study in France; upon graduation he returned to Chile and married Ana Waltemath the daughter of a wealthy German-Chilean family, they had a son named Luis Patricio.
He issued 2 sons:[3] his older son Nicolás Barrios-Lynch became a renowned educator in Argentina and a pioneer of the rural libraries movement across South America, while his younger son Luis Patricio Lynch Waltemath became a successful businessman in Chile.[4]