Data protection is data protection. At least so long as the UK is still a Member State. And even then, who knows. Given the data which the passenger shares with DHS (CBP) in order to obtain GE, I'm not certain that the data the air carrier shares about the passenger, also with the passenger's permission, is particularly more significant. Clearly LH doesn't think so.
Pressure from UK high-value customers who can use their GE to access Pre-Check when flying AA back to the UK will become pretty hefty. It's not just the length of the line, but the very limited scope of the TSA search (no shoes and jackets removed, no need to remove laptop or 3-1-1 bag, no MMW) that really attracts people.