The moment Lee was finally safe, his mind calmed down in an instant, and all of the sudden, all the pieces of the puzzle fell into place.
Ignoring their conversation, Han Jin's behavior during the meals and even her own father never addressing his child as his son, but calling her name – everything indicated there was something wrong with the situation. The weird request for the talk was the most glaring sign, but now Lee understood where it came from.
The fact that Han Jin was a girl was probably a secret known only to a handful of people. She was born after Han Zeming left and apparently the patriarch decided to appoint her to become his heir, while raising as a boy. Lee had no clue when or if it was planned to reveal her real identity, but old Finnie, before getting killed, was probably the only mother-figure the poor girl had.