Deformation and fracture processes in engineering materials often require simultaneous descriptions over a range of length and time scales, with each scale using a different computational technique. Here we present a high-performance parallel 3D computing framework for executing large multiscale studies that couple an atomic domain, modeled using molecular dynamics and a continuum domain, modeled using explicit finite elements. We use the robust Coupled Atomistic/Discrete-Dislocation (CADD) displacement-coupling method, but without the transfer of dislocations between atoms and continuum. The main purpose of the work is to provide a multiscale implementation within an existing large-scale parallel molecular dynamics code (LAMMPS) that enables use of all the tools associated with this popular open-source code, while extending CADD-type coupling to 3D. Validation of the implementation includes the demonstration of (i) stability in finite-temperature dynamics using Langevin dynamics, (ii) elimination of wave reflections due to large dynamic events occurring in the MD region and (iii) the absence of spurious forces acting on dislocations due to the MD/FE coupling, for dislocations further than 10 angstrom from the coupling boundary. A first non-trivial example application of dislocation glide and bowing around obstacles is shown, for dislocation lengths of similar to 50 nm using fewer than 1 000 000 atoms but reproducing results of extremely large atomistic simulations at much lower computational cost.