Since this answer hasn't seen much love here, I'm cross-posting answers from the linked FlyerTalk forum post made by OP.
While not an answer specific to Lufthansa, one poster states:
Most carriers are extremely lenient with soft side carriers as they
can be squeezed in spaces that a hard sided carrier will not fit in.
In fact AA even mentions this fact on their site where they say, "The
maximum size for cabin pet carriers is 19" long x 13" wide x 9" high.
Soft-sided pet carriers such as Sherpa bags may exceed these
dimensions slightly because they are collapsible."
However, Lufthansa is part of Star Alliance while American Airlines is part of oneworld, and they are different airlines anyway so policies could differ.