If this is a Oneworld Explorer or a Global Explorer, then it's very illegal.

Can be corrected by changing your first LAX to London. That way, youre going in one continuous direction. It would be a 4-continent business class, which runs about 3800 out of eastern europe, 7300 out of Ireland, 5000 out of western europe, and 4400 out of Gibraltar. Plus tax, of course.