BEagle...
I know the LAX was initially planned to stop in JFK, but subsequently deemed unnecessary... Obviously the LAX-LHR leg will tend to be further south than Great Circle.
I don't know what you fly / flew. However, from my 4 Eng days, this was no problem with 3 continuing, so long as the obvious further failures were looked at. It is SOP, accepted by the authorities, and carried out more often than you might think. The BA example I gave is recent, but I know there are others...
What are your concerns? It is a 4 Eng aircraft, a single explainable failure, secured, after the point where 4 engs are required. We now have a 3 eng aircraft, which equates to a TriStar / DC10 / MD11, and still having a level of redundancy superior to a twin. In the event of a further failure, we are down to 2. The aircraft would still cruise, albeit at a lower level, use more fuel (allowed for), and can be landed fine via a regularly practiced profile.
I am all for not pushing airmanship boundaries, and I was initially surprised at this SOP. However, having then thought it through, you are still more failures away from a problem in a 3 engine 747, than a 2 engine 777!
Each case will need to be looked at for it's merits - both the cause of the failure, and as you say, the routing, weather etc. However, bearing in mind that 3 Engs is not an emergency, no justification can be made for landing overweight, and therefore, even with dumping (which rarely gets you to MLW), you are going to have to fly for some hours. Might as well be going somewhere...