Answer, inelegant but effective.

const toggleList = document.getElementById("toggleList");
const listDiv = document.querySelector(".list");
const descriptionInput = document.querySelector("input.description");
const descriptionP = document.querySelector("p.description");
const descriptionButton = document.querySelector("button.description");
const listUl = listDiv.querySelector("ul");
const addItemInput = document.querySelector("input.addItemInput");
const addItemButton = document.querySelector("button.addItemButton");
const lis = listUl.children;
const firstListItem = listUl.firstElementChild;
const lastListItem = listUl.lastElementChild;

function attachListItemButtons(li) {
  let up = document.createElement("button");
  up.className = "up";
  up.textContent = "Up";
  li.appendChild(up);

  let down = document.createElement("button");
  down.className = "down";
  down.textContent = "Down";
  li.appendChild(down);

  let remove = document.createElement("button");
  remove.className = "remove";
  remove.textContent = "Remove";
  li.appendChild(remove);
}

// function removes all button elements from the list items.
function resetButtons() {
  for (let i = 0; i < lis.length; i += 1)
    while (lis[i].lastElementChild) {
      lis[i].removeChild(lis[i].lastElementChild);
    }
}

//function checks the list items and removes the first child of the top one if it is an "up" button
// it also removes the last list items second child if its a down button;
function removeUnusedButtons() {
  let liFirst = lis[0];
  let upBtn = liFirst.firstElementChild;
  if (upBtn.className == "up") {
    liFirst.removeChild(upBtn);
  }

  let liLast = lis[lis.length - 1];
  let downBtn = liLast.firstElementChild.nextElementSibling;
  if (downBtn.className == "down") {
    liLast.removeChild(downBtn);
  }
}

//Function Calls on initial Run.
for (let i = 0; i < lis.length; i += 1) {
  attachListItemButtons(lis[i]);
}
removeUnusedButtons();
// Event Listeners

listUl.addEventListener("click", (event) => {
  if (event.target.tagName == "BUTTON") {
    if (event.target.className == "remove") {
      let li = event.target.parentNode;
      let ul = li.parentNode;
      ul.removeChild(li);
    }
    if (event.target.className == "up") {
      let li = event.target.parentNode;
      let prevLi = li.previousElementSibling;
      let ul = li.parentNode;
      if (prevLi) {
        ul.insertBefore(li, prevLi);
      }
    }
    if (event.target.className == "down") {
      let li = event.target.parentNode;
      let nextLi = li.nextElementSibling;
      let ul = li.parentNode;
      if (nextLi) {
        ul.insertBefore(nextLi, li);
      }
    }
  }
});

toggleList.addEventListener("click", () => {
  if (listDiv.style.display == "none") {
    toggleList.textContent = "Hide list";
    listDiv.style.display = "block";
  } else {
    toggleList.textContent = "Show list";
    listDiv.style.display = "none";
  }
});

descriptionButton.addEventListener("click", () => {
  descriptionP.innerHTML = descriptionInput.value + ":";
  descriptionInput.value = "";
});

addItemButton.addEventListener("click", () => {
  let ul = document.getElementsByTagName("ul")[0];
  let li = document.createElement("li");
  li.textContent = addItemInput.value;
  attachListItemButtons(li);
  ul.appendChild(li);
  addItemInput.value = "";
});
// Added the event listener here for simplicity sake, on clicking any button inside the list area it resets buttons 
// attaches buttons to each list item and removes the up and down buttons from the end.
listDiv.addEventListener("click", (e) => {
  if ((e.target.tagName = "BUTTON")) {
    resetButtons();
    for (let i = 0; i < lis.length; i += 1) {
      attachListItemButtons(lis[i]);
    }
    removeUnusedButtons();
  }
});