The National Museum of Korea is huge — you'll walk for hours across its galleries and grounds — so it's worth dropping your bags first. It sits by Ichon Station (Line 4), and the coin lockers there are the easiest place to leave a suitcase.
Ichon Station coin lockers
Ichon Station has T-Locker coin lockers at 2 spots, about 25 in total — not many, so on weekends or busy days check what's free, by size, on the Ichon Station page before you go. Prices are the standard Seoul rate — about ₩2,200 (small) to ₩4,400 (large) for four hours. English screen, card, no ID.
The museum's own lockers
Because the museum is large and popular, it also has visitor lockers near the entrance — handy for coats and day-bags. Availability and terms vary, so check on site; for a full suitcase, the station lockers (or a station with more large units) are safer.
Good to know
Admission to the permanent galleries is free. With only ~25 lockers at Ichon, if they are full use the museum's own storage, or see the full Seoul luggage storage guide.
Sources: prices, sizes and hours from the Seoul Metropolitan Government (T-Locker); spots, counts and availability from Seoul Open Data. Check official museum info for its facilities.