The main objective of this work is to develop an adaptive mesh refinement technique in a new HPC framework kalypsso-lbm to allow the simulation of complex single-component two-phase flows (Navier-Stokes-Korteweg) using a finite-difference lattice Boltzmann method. The main difficulty of simulating such flows lies in the ability to completely resolve the diffuse phase-interface where abrupt but still continuous variation of the solution occurs. To ensure sufficient resolution at the phase-interface, standard numerical methods relying on uniform meshes lead to over-resolved areas in the bulk of each phase impeding the practicality of the model for complex simulations. The development of a new MPI scalable adaptive mesh refinement (AMR) framework using p4est for core AMR algorithms [1] as well as the C++ performance portability library Kokkos [2] for shared memory parallelism in kalypsso [3] is extended to lattice Boltzmann methods [4] to allow efficient mesh adaptation of the solution by keeping the phase-interface region at a sufficiently high resolution while allowing mesh coarsening in other fluid regions where the discretization error is lower. The reduction in total number of cells provided by the optimal placement of computational resources allows important reduction in computation times and memory requirements while maintaining the solution accuracy obtained by uniform meshes as can be seen in figure 1. In addition, by off-loading computations on the GPU, kalypsso-lbm simulation runtimes may be further reduced by a factor 5.