A saying reputed to be of around WWII era.
Said to a person when they're busy wasting their time running their
mouth off complaining over a usually trivial matter.
Meaning:
Much like a child
pouts their
lower lip when they're not getting their way, "Walking on your lower lip" implies their lip is so far pouted, they risk tripping over it.
"Life is so hard, I can never get ahead, everyone is
against me, I'm not popular, and it's all
the government's fault"
"Bah, stop
walking on your lower lip and do something useful".