Recently van Dokkum et al. (2018b) reported that the galaxy NGC 1052-DF2 (DF2) lacks dark matter if located at $20$ Mpc from Earth. In contrast, DF2 is a dark-matter-dominated dwarf galaxy with a normal globular cluster population if it has a much shorter distance near $10$ Mpc. However, DF2 then has a high peculiar velocity wrt. the cosmic microwave background of $886$ $rm{km,s^{-1}}$, which differs from that of the Local Group (LG) velocity vector by $1298$ $rm{km,s^{-1}}$ with an angle of $117 , ^{circ}$. Taking into account the dynamical $M/L$ ratio, the stellar mass, half-light radius, peculiar velocity, motion relative to the LG, and the luminosities of the globular clusters, we show that the probability of finding DF2-like galaxies in the lambda cold dark matter ($Lambda$CDM) TNG100-1 simulation is at most $1.0times10^{-4}$ at $11.5$ Mpc and is $4.8times10^{-7}$ at $20.0$ Mpc. At $11.5$ Mpc, the peculiar velocity is in significant tension with the TNG100-1, TNG300-1, and Millennium simulations, but occurs naturally in a Milgromian cosmology. At $20.0$ Mpc, the unusual globular cluster population would challenge any cosmological model. Estimating that precise measurements of the internal velocity dispersion, stellar mass, and distance exist for $100$ galaxies, DF2 is in $2.6sigma$ ($11.5$ Mpc) and $4.1sigma$ ($20.0$ Mpc) tension with standard cosmology. Adopting the former distance for DF2 and assuming that NGC 1052-DF4 is at $20.0$ Mpc, the existence of both is in tension at $geq4.8sigma$ with the $Lambda$CDM model. If both galaxies are at $20.0$ Mpc the $Lambda$CDM cosmology has to be rejected by $geq5.8sigma$.
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