OK, I thought not but worth checking. Now how about this scenario. Until I did my JAR ATPLf, I was skipper of the yacht also owned by the Lear owner. Can he employ me as yacht manager (which would genuinely be the case when not flying), and then I fly the Lear for free on my FAA PPL?
The issue isn't reward as in the UK, but for compensation or hire. The FAA has determined that compensation includes the logging of flight time...even logging the time will be construed as compensation.
Understand you're operating this aircraft outside the US. You'll require at least a SIC type rating in the aircraft. You're acting as a required crewmember. You receive compensation from the owner as his yacht skipper, and the idea that you can backdoor the compensation issue by saying that's what you get paid for, and not the flying just won't wash. The FAA doesn't buy it, and has provided as much in their chief counsel legal interpretations on the matter.
The FAA provides additional tests, such as determining if you were going to make the trip with or without the owner present. In other words, were you going there in the first place, and this is nothing more than an alternate means of getting there? No...you're going somewhere because the boss is going there, and this is part of your employment...it's compensation or hire, no matter how you slice it. Even donating the time...compensation or hire.
You could sidestep that part of the issue by sharing the costs...but you'd have to pay a pro-rata share of the cost of operating the airplane. You probably don't want to do that.
Look at it from a different perspective. Why not operate it from your ATPL? Your JAR ATPL will require a type rating in the airplane, too. This is time and expense; more than obtaining the commercial pilot certificate would require, in fact. I'm not familiar enough with the JAR regulation to know if you would be allowed to pilot an N registered airplane on your European certificates...but you can certainly pilot any other national registration on an FAA certificate, so far as the FAA is concerned (other country's regulations not withstanding). Does the regulation where you are operating require that you hold an FAA certificate to fly the N registered airplane outside the United States? The FAA doesn't care, nor require that a pilot hold a FAA certificate to fly an N registered airplane.
The question then might be why not make the arrangements to fly it on your ATPL?
The private pilot certificate in the US does not grant privileges of working for compensation or hire. Any other private pilot that flies along with your boss is subject to the same arrangements, including the requirement to obtain an SIC type rating (at a minimum) to act as a required crewmember in the Learjet. If you don't log the time and you don't accept any other compensation, and you can conclusively show that your flying with this individual is purely for fun and not in any way, shape, nor form connected with your employement (difficult to do, if this man is your boss), you may be able to get away with it, legally.
If you're going to fly as SIC, however, you ought to at a minimum be obtaining the proper training for the airplane and attending a course. You can get away with minimal training, an oral, and three bounces in the airplane (but must walk the paper into the FSDO for the SIC type...which may be a problem outside the US)...but if you're flying an advanced turbojet airplane you really should be going to FSI or Simuflite and doing it properly. If you go that route, get the commercial done while you're there, or get the ATP added on as part of the type ride, and you're done.