You can not use double quotes in the chain that you are enclosing with them, I explain, the correct thing would be:
document.getElementById("my_element").innerHTML = '<li id="my_li">.../li>';
or
document.getElementById("my_element").innerHTML = "<li id=\"my_li\">.../li>";
Any of the 2 examples will work for you.
Under the fact that you do not leave much code to check where you are making the mistake, I can only give you some examples of how to do it.
Here is an example made with jQuery:
$(document).ready(function () {
$("button").on("click",function () {
$("ul").html('\
<li id="My_li_a">lista a</li>\
<li id="My_li_b">lista b</li>\
<li id="My_li_c">lista c</li>\
');
setTimeout('alert($("#My_li_a").text());',100);
});
});
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<ul id="My_Element">
<li>lista 1</li>
<li>lista 2</li>
<li>lista 3</li>
</ul><br>
<button>cambar lista</button>
or if you prefer javascript:
function changeList() {
document.getElementById("My_Element").innerHTML='\
<li id="My_li_a">lista a</li>\
<li id="My_li_b">lista b</li>\
<li id="My_li_c">lista c</li>\
';
setTimeout('alert(document.getElementById("My_li_a").innerHTML);',100);
};
<ul id="My_Element">
<li>lista 1</li>
<li>lista 2</li>
<li>lista 3</li>
</ul><br>
<button onClick="changeList()">cambar lista</button>
Compare this code with yours and you will find the error, Regards ..;))