The connection is that sshd calls code in libsystemd when running as a systemd service, to notify systemd that it finished starting. An unrelated functionality in libsystemd (my guess is that it's related to parsing journald logs, since they can use LZMA compression) uses the lzma library, so libsystemd is linked against it. That is, the chain is: sshd is linked against libsystemd, which is linked against liblzma. When loading the sshd executable, the dynamic linker will load all these libraries.

The backdoor was added to initialization code in liblzma (which runs whenever the dynamic linker loads that library). So that malicious code runs before sshd starts executing, and manipulates the dynamic linker so that it will do something (which is still being analyzed AFAIK) when some specific functions are called by the sshd executable.

Apparently liblzma in the compromised tarball would search for sshd functions and replace them with their own versions. This normally doesn't happen for the reason I've described, but many distros tend to compile sshd with a plugin that makes use of libsystemd, which depends on liblzma and therefore sshd will be linked with liblzma in that case. Liblzma could have done anything else it wanted, so the limited reach of this vulnerability is actually a better scenario...

Yes.