Of course every flight is different, and it depends on the day and the weather conditions, but I don't recall the turbulence being any worse on LAX
(and return) than on any other transoceanic flight. The flight is long enough and will pass through enough different areas of weather that the odds are the seatbelt sign will be on at some point or another, but I don't think you have anything in particular to worry about. Mostly I remember those flights being long and boring with very little to look at out the windows. Who knows, after 10 hours or so you might find yourself wishing for some bumps just to liven things up a bit.
I don't love turbulence either (actually, I hate it!), but I've learned that it doesn't help to overthink it. I used to look at weather forecasts to try and figure out if my flights would be smooth or not, and most of the time I was wrong. Turbulence is very hard to predict, but keep in mind that most flight crews don't enjoy being jostled around either, and will do their best to find a smooth ride for you. If that's not possible, know that as long as you keep your seatbelt on when indicated, there's really no danger.
Enjoy your trip--you'll have a great time!
Common sense is not so common. -Voltaire