<ul>
    <li class="lession">
        <div class="lname">Geography</div>
        <span class="lstatus"></span>
        <span class="lstart">8:00</span> - <span class="lfin">8:40</span>
    </li>
    <li class="lession">
        <div class="lname">Chemistry</div>
        <span class="lstatus"></span>
        <span class="lstart">8:50</span> - <span class="lfin">9:30</span>
    </li>
    <li class="lession">
        <div class="lname">Russian language</div>
        <span class="lstatus"></span>
        <span class="lstart">9:40</span> - <span class="lfin">10:20</span>
    </li>
    <li class="lession">
        <div class="lname">Literature</div>
        <span class="lstatus"></span>
        <span class="lstart">10:30</span> - <span class="lfin">11:08:35</span>
    </li>
</ul>

function getdatebytime(str) {
  let date = new Date(), x;
  if ((x = str.match(/^\s*(\d+):(\d+)(:(\d+))?\s*$/))) {
    date.setHours(x[1], x[2], x[4]||0);
  }
  return date;
}

// Заполняем хранилище расписания
let  data = [];
for (let l of document.querySelectorAll('.lession')) {
  data.push({
    html_element: l.querySelector('.lstatus'),
    start: getdatebytime(l.querySelector('.lstart').innerHTML),
    fin: getdatebytime(l.querySelector('.lfin').innerHTML),
  })
}

function handle() {
  var date = new Date(), status = '', next = false;
  for (let l of data) {
    if (date < l.start) {
      status = 'Upcoming';
      if (!next || l.start < next) next = l.start;
    } else if (date < l.fin) {
      status = 'Going';
      if (!next || l.fin < next) next = l.fin;
    } else {
      status = 'Complete';
    }
    if (l.html_element) {
      l.html_element.innerHTML = status;
    }
  }
  if (next) {
    let interval = next - date;
    if (interval > 60000) interval -= 60000; // за минуту до срока, чтобы сильно не промазать
    setTimeout(handle, interval);
  }
  // console.log(next,date);
}

handle();