Mihai obtained the Wintgen inequality, also known as the generalized Wintgen inequality, for Lagrangian submanifolds in complex space forms and also characterized the corresponding equality case. Submanifolds $M$ which satisfy the equality in these optimal general inequalities are called generalized Wintgen ideal submanifolds in the ambient space $\tilde M$. For generalized Wintgen ideal Lagrangian submanifolds $M^n$ in complex space forms $\tilde M^n(4c)$, we will show some properties concerning different kinds of their pseudosymmetry in the sense of Deszcz.