<style>
  body{background: white;}
  #changebgcolor{
    width:100px;
    height:100px;
    background: white;
    border: 1px solid lightgray;
  }
</style>
<div id="changebgcolor"></div>

let block = document.getElementById('changebgcolor');

let count = 0;
function handlerClick(){
  let bgColors = ['red', 'blue', 'yellow']; // цвета какие нужны

  count = (count > bgColors.length)? 0 : count;
  block.style.backgroundColor=bgColors[count]
  count++;

}
block.addEventListener('click', handlerClick)

function ChangeColor(Element) {
    let text = document.getElementById('lol');

    if(text.style.color === 'green') text.style.color='red';
    else text.style.color ='green';

    return false;
}