Another way to look at it:

The kernel has built-in-miniroot with "mini-init" and initial dhcp
client (all in the same program).  dhcp does its thing, locates the
diskless "mother", mounts it, and chroots into it, dropping lease info
into the appropriate directory somewhere.  Still as pid 1, it then
exec's the "real" init out of the network-mounted root; rc then runs a
"real" dhcp client which inherits the lease from the initial dhcp
client.  Something else then causes the miniroot, which nothing can
access any more, to get garbage-collected.