Assuming the menu option has a suitable CSS selector e.g. "item-135", it could be hidden via CSS.
You could create a custom HTML module to add the appropriate code to the applicable page(s). Set the custom HTML module position to "debug" or similar if your template has this option (as the debug module position is less likely to have any margins or padding associated with it).
Install and enable the Regular Labs Sourcerer plugin or similar so the code is not stripped from your Custom HTML Module.
In the Custom HTML Module, your code will look something like this:
{source}
<?php
if ([some condition]) {
$document = JFactory::getDocument();
$style = '.item-135 {display: none;}';
$document->addStyleDeclaration ($style);
}
?>
{/source}