You can find for any element inside element with .querySelectorAll as below.

if (pickNewUl.querySelectorAll('#' + listItems[i].id).length === 0) {
    // Add element    
}

Reference : https://developer.mozilla.org/en-US/docs/Web/API/Document/querySelectorAll

Your complete code should be like below.

const pickNewUl = document.getElementById("ullist1"); 
if (pickNewUl.querySelectorAll('#' + listItems[i].id).length === 0) {   
    var createLi = document.createElement("li");
    createLi.id = listItems[i].id;
    createLi.classList.add(pickNewUlsl);
    createLi.innerHTML = listItems[i].textContent; 
    createLi.innerHTML += "<a onclick='remove(this)' class='removebtn'>X</a>";
    pickNewUl.appendChild(createLi);
}

You can just wrap you code inside an if:

// the same as before but using pickNewUl instead of document
if (!pickNewUl.getElementById(listItems[i].id)) {
  const createLi = document.createElement("li");
  ...
  pickNewUl.appendChild(createLi);
}

Btw, I suggest to use a different approach excluding duplicated id:

// The string into querySelector method is a template string.
if (!pickNewUl.querySelector(`[data-item-id="${listItems[i].id}"]`)) {
  const createLi = document.createElement("li");
  createLi.dataset.itemId=listItems[i].id;
  ...
  pickNewUl.appendChild(createLi);
}