If you want all the li tags in an array even when they are in different ul tags then you can simply do
var lis = document.getElementByTagName('li');
and if you want to get particular div tag li's then:
var lis = document.getElementById('divID').getElementByTagName('li');
else if you want to search a ul first and then its li tags then you can do:
var uls = document.getElementsByTagName('ul');
for(var i=0;i<uls.length;i++){
var lis=uls[i].getElementsByTagName('li');
for(var j=0;j<lis.length;j++){
console.log(lis[j].innerHTML);
}
}