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".