He even gives the definition for the L=1 Lipschitz condition afterwards.
Lipschitz continuity means the differential quotient is globally bounded (where it exists). Differentiability, by definition, means the differential quotient converges at every point.
Lipschitz continuity means the differential quotient is globally bounded (where it exists). Differentiability, by definition, means the differential quotient converges at every point.
These are somewhat related, but different things.