If you have a paid membership at United Club, you will be able to access the Lufthansa Business lounge in MXP if you meet the following:

Following section taken from Star Alliance site:

As an eligible holder of Paid Lounge Membership, you have access to any Star Alliance member airline Business Class Lounge. Eligible paid memberships include United Club and Air Canada Maple Leaf Club – Worldwide. You will need to show your boarding pass for a Star Alliance flight departing from the local airport together with your valid eligible paid lounge membership card, displaying the Star Alliance Lounge Logo. You are entitled to a maximum of one guest. Except in Singapore where the Singapore Airlines Krisflyer Gold Lounge is available.