list.jsx

    if (!_.has(this.cache, page)) {
      const requestWithAttributes =
        _.reduce(
          _.toPairs(requestAttributes)
          , (acc, [a, b]) => acc + a + "=" + b + "&"
          , request(userInfo) + "?");

      fetch(requestWithAttributes)
        .then((resp) => resp.json())
        .then((result) => this.cache[page] = result);
      console.log(this.cache);
      /* Object
       * 0 : Array[30]*/
      console.log(this.cache[page]);
      /* undefined*/
    }

le code est asynchrone dans ton fetch :

fetch(requestWithAttributes)
        .then((resp) => resp.json())
        .then((result) => {
            this.cache[page] = result
            console.log(this.cache);
            console.log(this.cache[page]);
        });

avec async / await :

const maFonction = async () => {
  const resp = await fetch('./data')
  const result = await resp.json()
  this.cache[page] = result
  console.log(this.cache);
  console.log(this.cache[page]);
}