Hide a Menu Item on Login

Can’t you change CSS rules?

.hide-item-not-login{
    display: block !important;
}

.logged-in .hide-item-not-login{
    display: none !important;
}

EDIT

To add login/logout menu item, you will need to add one more class to logout menu item. Let’s say you added class .logout-link to logout menu item.
Then you can add css like this.

.hide-item-not-login{
    display: block !important;
}

.logged-in .hide-item-not-login{
    display: none !important;
}

.logout-link{
    display: none !important;
}

.logged-in .logout-link{
    display: block !important;
}