I don't really see where you are using any of the suggestions from the linked post in your code on the page you linked to. Perhaps I missed it.
In any case, since you are using a select element's onchange event to load the Ajax content, that is where you should set the:
window.acInit=false;
Code:
<select id="mainSelection" onchange="window.acInit=false;populateSubSelection()" name="s1">
<option>Visualizza per</option>
<option value="problema">Problematiche</option>
<option value="prodotto">Prodotti</option>
</select>
Then on the inserted content page, the links that fire lytebox (which I couldn't find) or their container should have the mouseover initialization event that also sets:
window.acInit=true;
Code:
onmouseover="if(!window.acInit){initLytebox();window.acInit=true;};"
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