All three airline alliances have Rome on sale from San Francisco and San Jose airports in mid-to-upper $400s for travel from late September to April 2019. From LAX, Star Alliance prices tickets to Rome mostly in upper $400s, while Norwegian has nonstop flights to Rome as low as $402 round trip with $420s from October to March 2019.
I have noticed this week that many of the ticket prices showing up on Google Flights are not pricing out as shown, often increasing by $50 to $100s more than shown. You might need to play around with dates and flights to find the lower ticket prices in $400s and try OTA sites like Momondo.com and others.
United Airlines Los Angeles LAX – Newark EWR – Rome FCO – Zurich ZRH – LAX
$443.81 round trip Tue Feb 5 – Tue Feb 12
(note: Return flight on Swiss Airlines only earns miles with Miles&More. No Mileage Plus miles.)
Delta Airlines San Jose SJC – LAX – Rome FCO (Alitalia) – Amsterdam AMS (KLM) – Seattle SEA – SJC
$462.01 round trip Sun Oct 7 – Wed Oct 17
If you can travel with only a carry-on bag, then Norwegian has lowest fares at $185 one way from LAX in October.
Norwegian Airlines LAX-Rome FCO one way $184.90 Wed Oct 24
Use miles for the return flight or pay $216.25 through an OTA site or $234.90 through Norwegian.
British Airways AARP discount rates are available too from SJC and SFO.
San Jose SJC – Dallas DFW – Rome FCO – DFW – SJC
$471.74 round trip Tue Oct 2 – Thu Oct 11
