LONDON—As pick-up lines go, this one takes some beating: “You have an interesting face. I would like to do a portrait of you. I am Picasso.”

This was delivered spontaneously outside the Galleries Lafayette department store in Paris as Pablo Picasso encountered a 17-year-old girl from a Paris suburb named Marie-Thérèse Walter. He was 45, already established as the most dominant and original force in modern painting. She had no idea who he was.

Picasso was a skilled seducer, with a primitive attitude toward women, but this encounter in 1927 was to be one of the most consequential in his life.