  We prove the existence of flips for $\mathbb Q$-factorial NQC generalized lc
pairs, and the cone and contraction theorems for NQC generalized lc pairs. This
answers a question of C. Birkar which was conjectured by J. Han and Z. Li. As
an immediate application, we show that we can run the minimal model program for
$\mathbb Q$-factorial NQC generalized lc pairs. In particular, we complete the
minimal model program for $\mathbb Q$-factorial NQC generalized lc pairs in
dimension $\leq 3$ and pseudo-effective $\mathbb Q$-factorial NQC generalized
lc pairs in dimension $4$.
