Having played around with these fares a bit something that may be of help with anyone looking to piece these together - if you depart MXP with LX you need to book the trip in P class however if you depart on LH it books to Z which is 1 booking class higher - price is essentially the same (about £10 more on LH) however it allows you to book higher booking classes on LH and UA flights so makes availability easier to find.
had a look earlier and departing may you can do MXP-LAX-AKL-TYO-MXP for £2700ish which is an unbelievable fare.