p.1 #5 · Are you getting the crisp images you expect from your 50mm Summilux Asph?
Were they both shot wide open? The Lux doesn't look at all stopped down, which would help explain things.
Otherwise, the APO-Lanthar has, like the Otus 55, wonderfully slow focus roll-off, to the point where it feels like you're cheating, getting more depth than you should at that focal length and speed. The Lux is a great lens, but it's not that kind of lens.
The Lux shot looks out of focus. I would have also thought that maybe there was camera movement, but her thumb seems sharper than her eyelashes in the Lux shot.
Try a tripod comparison with very careful best-of-three focusing.
Midzone with the 50 Lux is softer than the center at wide apertures at close distance (and focus and recompose will make it worse). The Lanthar is very flat field across the frame at f/2.
DOF looks very different for these shots – are you comparing f/1.4 on the Lux with f/2 on the Lanthar?
p.1 #9 · Are you getting the crisp images you expect from your 50mm Summilux Asph?
It was really bothering me, so I took it out for a real world test today alongside a couple of other 50s. Nothing clinical like Fred’s lab style tests, just straight hands on, real world shooting. It’s amazing what you end up doing with your time when you're retired!