rita,
<!DOCTYPE html>
<html>
<head>
<meta name="viewport" content="width=device-width, initial-scale=1">
<meta charset="utf-8">
<style>
* {
box-sizing: border-box;
}
#show_box {
display: none;
color: #0000FF;
}
#show_box.open {
display: block;
}
</style>
</head>
<body>
<center>
<ul id="my_All">
<li class="li_a" style="display:none">HELLO 1</li>
<li class="li_a" style="display:none">HELLO 2</li>
<li class="li_a" style="display:none">HELLO 3</li>
</ul>
<div id="show_box">Нужно показать!!!</div>
</center>
<script>
let show_box = document.getElementById('show_box');
let open = [...document.querySelectorAll('#my_All .li_a')].every(li => getComputedStyle(li).display === 'none');
show_box.classList.toggle('open', open);
</script>
</body>
</html>