I'm not a SEN, just a measly A3*G, but based on what I've read/heard LH really only upgrades when there is absolutely no other option.
Was upgraded once on a full flight from MUC to EWR when the A359 was swapped for an A346. I was booked in PE which was now needed to accomodate the Y passengers (the A346 has fewer Y seats than the A359) and got bumped into C at the gate.
This is pretty consistent with what I've heard from friends that are SENs as well.
Unlike other airlines (especially the US ones obviously), LH rather flies with their premium cabins empty instead of upgrading their (or any) frequent flyers.
I guess that's what being a monopolist gives you...