We find N = 1 Lagrangian gauge theories that flow to generalized Argyres-Douglas theories with N = 2 supersymmetry. We find that certain SU quiver gauge theories flow to generalized Argyres-Douglas theories of type (A(k-1), A(mk-1)) and (I-m,I-km, S). We also find quiver gauge theories of SO/Sp gauge groups flowing to the (A(2m-1), D2mk+1), (A(2m), D2(m(k-1)+k)) and D-m(2k+2)(m(2k+1))[m] theories.