We consider the Cauchy problem associated to the fourth-order nonlinear Schrödinger-Hartree equation with variable dispersion coefficients. The variable dispersion coefficients are assumed to be continuous or periodic and piecewise constant in time functions. We prove local and global well-posedness results for initial data in $ H^s $-spaces. We also analyze the scaling limit of the fast dispersion management and the convergence to a model with averaged dispersions.