It seems that Lese is a feminine word. However, its genetive (plural) seems to be des Lesens instead of der Lesen. I’ve read in my grammar book that for feminine words the Genitive should be in the form of der alten Tanten. So has my grammar book made a mistake? Or is it I got the example wrong. Or is there some exception to this rule?
It seems you mixed up several concepts.
There is a feminine word die Lese (meaning the process of collecting, usually grapes for making wine). Its genitive plural is indeed der Lesen.
There is a neutral word das Lesen (meaning the act of reading, sometimes also the act of collecting), the nominalized infinitive of lesen. It does not have a plural.
Des Lesens is the genitive singular of das Lesen.