A new hybrid computational fluid dynamics (CFD) / computational aeroacoustic (CAA) method is presented, in which the flow field is predicted by a lattice Boltzmann method and the acoustic wave generation and propagation is simulated by a numerical solution of the acoustic perturbation equations (APE) [1]. A drawback of the solution procedure with two separate solvers is the necessity to transfer the acoustic source terms obtained from the instantaneous flow field from the CFD to the CAA solver as these source terms are defined in a subvolume of the acoustic domain typically requiring huge storage capacities. An exchange via disk I/O is inefficient on high-performance computing hardware since the overall parallel scalability is often limited by the available I/O bandwidth. To avoid this disadvantage, a fully-coupled direct-hybrid method has been developed in~[5] conducting the CFD and CAA simulations in a shared framework. The newly developed method is based on this previous work, where a finite-volume (FV) solver for the Navier-Stokes equations was used for the CFD method and a concurrent and interleaved execution of the CFD and CAA solvers exchanging acoustic source terms in-memory and thus fully avoiding disk I/O was implemented. In this solver framework, a joint hierarchical Cartesian grid is partitioned on a coarse level via a space-filling curve such that the CFD and CAA solvers are efficiently coupled and parallelized, also enabling dynamic load balancing [3]. Since the lattice Boltzmann (LB) method is well-known as an efficient low Mach CFD solver, a new direct-hybrid CFD/CAA method has been developed, based on an LB method for the flow field prediction coupled to a discontinuous Galerkin (DG) scheme solving for the APE [2]. The coupling strategy is similar to a previously developed direct-hybrid CFD/CAA method [4] with a finite-volume solver for the Navier-Stokes equations. However, a major difference for the coupling procedure arises from the time stepping method. While the finite-volume method is based on a multi-stage Runge-Kutta method, the LB method predicts a new solution in a single step. In this paper, the results from the application of the two direct-hybrid methods in terms of accuracy and computational efficiency will be summarized.