Why are reading fairy tales so lewd?
The original dialog use お伽話 (otogibanashi), commonly translated as "fairy-tale".



The Japanese-English online dictionary, Jisho only states 1 meaning which is the most common usage:


  fairy-tale; nursery-tale


However, when referring to the Japanese-Japanese online dictionary, Kotobank, it states 2 meanings:


  
  A story (legend, folklore, etc.) for children to listen to. "Momotaro", "Kachi-kachi Yama"-type. Alternatively, as a trope, a fantastical story that ignores realism.
  A story which takes place while doing otogi.
  




In fact, when Aida told Eto about "doing otogibanashi at night", Eto was surprised, realizing it's about togi. (The translation is wrong, Eto didn't shout otogibanashi, only togi)



Now, what is (o)togi? Otogi is basically o (honorific prefix) + togi. Jisho states:


  
  Otogi: attending (upon); keeping another company​
  Togi: nursing; nurse; attending; attendant; entertainer​
  


While Kotobank states:


Otogi


  
  Accompanying other to kill time during the night. Alternatively, the person who does that.
  Attending someone's bedroom. Alternatively, the person who does that. Concubine; mistress​.
  [...]
  [...]
  

Togi


  
  Become a chat partner, humoring and entertaining them. Alternatively, the person who does that. Otogi.
  Attending someone's bedroom. Alternatively, the person who does that.
  [...]
  [...]
  





So, yes, it means Iono-sama invites Eto to accompany her at night, possibly also in her bedroom as a concubine, which is Iono-sama's objective from the beginning. Considering the nature of Iono-sama, it's not really surprising if it has something to do with lewd things...