Recently published results demonstrated that the Lévy Flight Firefly Algorithm (LFFA) can be effectively applied to IIR adaptive filter structures designed with parallel or cascade second order sections. Recently published results also demonstrated that the LFFA can be effectively used for IIR adaptive filters designed with second order coupled form sections. This paper now proposes that bio-inspired optimization algorithms can be applied to FIR and IIR adaptive lattice-ladder structures, which have been well known throughout the literature for many past decades. Experimental results are presented to demonstrate that the LFFA performs effectively on several different types of adaptive lattice-ladder structures.