Korean Air flies from Terminal 4 at Heathrow, not Terminal 3 (that's Asiana's terminal).
You can
pay to use various Heathrow lounges but there is no such facility available to you in Terminal 4.
Korean uses the
Skyteam lounge in Terminal 4, which is accessible by anyone holding Skyteam Elite Plus status [and their guest(s)] departing Terminal 4 on a Skyteam flight, and by passengers in First and Business class departing Terminal 4 on a Skyteam flight.