Interesting thread.1or 2 on the nail.Check your FAR/AIM to start with.
1) Rules changed some 2 or 3 years back.Ref pressure from ICAO,now all Part 91 aircraft ref Lear/complex/2 crew types must have a full PIC or SIC Type rating on PPL;CPL or ATP. There is NO transference from JAA type to FAA type.Period.I have FAA/JAA Atps/PIC Typed on both. I checked with FSDO and FlightSafety,(USA),Regs dept last year. Don't talk yourself into a trap,and do read the endless small print in Insurance Covers.Your legal obligation to conform to the terms of your licence is to The FAA ONLY.
Not only FAA inspecters that could ramp check you,but so can JAA ones too.They are out to nail Part 91,sooner or later,so any excuse!!
My advice: get a cpl/atp and type rating (FAA). Lear is not a toy.It is a rocket,not a cessna 172 with a couple of Fans!! Good Luck.