Alitalia in business class on a direct flight would be great. Business class award space on the LAX-FCO route is hard to come by, though. If you want to book that with more miles and less cash, use DL to book the award. I believe it's 125k miles RT in business, but no fuel surcharges. Just ~$150 in taxes.

If that doesn't work out, looking for AA F/J awards LAX-JFK, then connecting to JFK-MXP on AA would also work. AA's business class isn't going to be as good as Alitalia's, though. AZ gets a bad rap, mostly for ground services, a terrible website, etc - but once you're in the air, it's very good. Probably the best business class food to Europe.

Since you already have 130k DL, you have enough for one ticket. I'd try and get that balance to 250k and book an AZ business class award, if you can find the space. West coast business class to Europe award space is generally rare on any carrier. But at least with DL's partners, you could fly direct on AZ or one stop on AF. I really enjoyed my last business class trip on AF. And if none of that pans out, you can buy a coach ticket to an east coast gateway and connect to a business class award.

EDIT: I see you said next summer. Award space in general is going to be tight, have a backup plan if you can't get a business class award. Economy might even be difficult, as summer is peak tourism season for US to Italy.