There is an Air Berlin low fare from Los Angeles to Venice, Italy via Dusseldorf flights from about $560 to $610 round trip for departures in November and December. I find these low ticket prices on Orbitz and CheapTickets and even under $550 through Momondo.com OTA sites, but Air Berlin quotes $700s for these same dates.
No guidance to offer for finding dates, except to hunt and peck. These low fare ticket dates do not show up on Google Flights or ITA Matrix. I tried a few dates in October and February and the price goes up to $700s on the OTA sites. Basically, November and early December departures are range of availability I was able to locate fares in $500s.
If you want to travel to Venice, Italy in November or early December, then give this fare a try.
Here are screenshots of ticket prices I found at 11:00am Pacific time.
Los Angeles – Dusseldorf DUS – Venice VCE – DUS – LAX
$559.52 round trip Orbitz.com Wed Nov 10-17
Los Angeles – Dusseldorf DUS – Venice VCE – DUS – LAX
$559.52 round trip Orbitz.com Wed Dec 1-8