Your code works well you just mistyped this line of code:
document.getElementbyId('lc').appendChild(element);
change it with this: (The "B" should be capitalized.)
document.getElementById('lc').appendChild(element);
HERE IS MY EXAMPLE:
<html>_x000D_
<head>_x000D_
_x000D_
<script>_x000D_
_x000D_
function test() {_x000D_
_x000D_
var element = document.createElement("div");_x000D_
element.appendChild(document.createTextNode('The man who mistook his wife for a hat'));_x000D_
document.getElementById('lc').appendChild(element);_x000D_
_x000D_
}_x000D_
_x000D_
</script>_x000D_
_x000D_
</head>_x000D_
<body>_x000D_
<input id="filter" type="text" placeholder="Enter your filter text here.." onkeyup = "test()" />_x000D_
_x000D_
<div id="lc" style="background: blue; height: 150px; width: 150px;_x000D_
}" onclick="test();"> _x000D_
</div>_x000D_
</body>_x000D_
_x000D_
</html>
_x000D_