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Our Universe may feature large-scale inhomogeneities and anisotropies which cannot be explained by the standard model of cosmology, that is, the homogeneous and isotropic FLRW metric, on which the $Λ$CDM model is built, may not describe accurately observations. Currently, there is not a satisfactory understanding of the evolution of the large-scale structure on an inhomogeneous background. We start the cosmology beyond homogeneity and isotropy (BEHOMO) project and study the inhomogeneous $Λ$LTB model with the methods of numerical cosmology. Understanding the evolution of the large-scale structure is a necessary step to constrain inhomogeneous models with present and future observables and place the standard model on more solid grounds. We perform Newtonian $N$-body simulations, whose accuracy in describing the background evolution is checked against the general relativistic solution. The large-scale structure of the corresponding $Λ$CDM simulation is also validated. We obtain the first set of simulations of the $Λ$LTB model ever produced. The data products consist of 11 snapshots between redshift 0 and 3.7 for each of the 68 simulations that have been performed, together with halo catalogs and lens planes relative to 21 snapshots, between redshift 0 and 4.2, for a total of approximately 180 TB of data. We plan to study the growth of perturbations at the linear and nonlinear level, gravitational lensing, cluster abundances and proprieties. Data can be obtained upon request. Further information is available at valerio-marra.github.io/BEHOMO-project .