Those are really pretty pieces of wood - the stock and the new lid. The rate at which wood dries is dependent on several factors. Some are relative humidity, temperature, air circulation and the size of the piece being dried. If a piece that size has not already checked, there is a good chance it will not. However, under average shop conditions, I would measure the air drying time from green to usable in years - not months. I would expect your lid to shrink across the grain as it continues to dry. It may also cup. The closer to quarter sawn the piece is - the less likely it is to cup. I would really like to be wrong on this one
Laurie