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No storage lockers, but there is a left luggage service, It is run by Chubb. I've used it a number of times. Last I used it, I think it was 80 baht per piece of luggage per day. The price may have gone up.
Bob's right, if you are going to stay at the same hotel at the end of your trip, you can leave your bags there. Any time I am coming back to Bangkok at the end of the trip, I do leave my excess bags at the hotel.