The spatial distribution of satellite galaxies around pairs of galaxies in the Sloan Digital Sky Survey (SDSS) have been found to bulge significantly toward the respective partner. Highly anisotropic, planar distributions of satellite galaxies are in conflict with expectations derived from cosmological simulations. Does the lopsided distribution of satellite systems around host galaxy pairs constitute a similar challenge to the standard model of cosmology? We investigate whether such satellite distributions are present around stacked pairs of hosts extracted from the ΛCDM simulations Millennium-I, Millennium-II, Exploring the Local Volume in Simulations, and Illustris-1. By utilizing this set of simulations covering different volumes, resolutions, and physics, we implicitly test whether a lopsided signal exists for different ranges of satellite galaxy masses, and whether the inclusion of hydrodynamical effects produces significantly different results. All simulations display a lopsidedness similar to the observed situation. The signal is highly significant for simulations containing a sufficient number of hosts and resolved satellite galaxies (up to for Millennium-II). We find a projected signal that is up to twice as strong as that reported for the SDSS systems for certain opening angles (∼16% more satellites in the direction between the pair than expected for uniform distributions). Considering that the SDSS signal is a lower limit owing to likely back- and foreground contamination, the ΛCDM simulations appear to be consistent with this particular empirical property of galaxy pairs.