With the old lacquer finishes, the alligatoring effect (commonly seen on pianos from the 1920s) resulted simply from exposure to light over the years. This is why an area such as the unseen back of a fallboard on a grand, looks perfectly normal--no light exposure there! Alligatoring does't stop, it keeps progressing over time. If it's a mild case, sometimes applying Liquid Gold or a similar treatment will restore the finish's luster temporarily (only until the next application is needed), but the only real solution is to strip the case and refinish it which is an expensive undertaking.