The Russian, ranked 14th in the world, traded opening service games with the South Korean before withdrawing with a back problem.
Lee faces Tamira Paszek of Austria for a place in the quarter-finals.
There was better news for fellow Russian Nadia Petrova after the fourth-seeded world number 18 beat Lourdes Dominguez Lino of Spain 6-2 6-4.
Petrova - who is in top seed Carolina Wozniacki's side of the draw - now plays Maria Jose Martinez.
The other remaining matches on Wednesday are second-round clashes, with third seed Kaia Kanepi beating Kazakh Galina Voskoboeva 6-2 6-2.
"I'm happy to win in two sets again. I think I played better today," Kanepi said. "I served better and felt better and wasn't nervous at all anymore.
"It's good to play two matches in a row. They were both around an hour and I don't have any injuries anymore, so things are going well right now."
The Estonian world number 16 faces Kiki Bertens in the quarters after the Dutchwoman beat Spaniard Silvia Soler 1-6 7-6 6-2 in their second-round match.
- Lourdes Dominguez Lino
- Tamira Paszek
- Kaia Kanepi