Lyman-α emitters (LAEs) are a promising probe of the large-scale structure at high redshift, z≳ 2. In particular, the Hobby-Eberly Telescope Dark Energy Experiment aims at observing LAEs at 1.9 <z< 3.5 to measure the Baryon Acoustic Oscillation (BAO) scale and the Redshift-Space Distortion (RSD). However, Zheng et al. (2011) pointed out that the complicated radiative transfer (RT) of the resonant Lyman-α emission line generates an anisotropic selection bias in the LAE clustering on large

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... s≳ 10 Mpc. This effect could potentially induce a systematic error in the BAO and RSD measurements. Also, Croft et al. (2016) claims an observational evidence of the effect in the Lyman-α intensity map, albeit statistically insignificant. We aim at quantifying the impact of the Lyman-α RT on the large-scale galaxy clustering in detail. For this purpose, we study the correlations between the large-scale environment and the ratio of an apparent Lyman-α luminosity to an intrinsic one, which we call the 'observed fraction', at 2<z<6. We apply our Lyman-α RT code by post-processing the full Illustris simulations. We simply assume that the intrinsic luminosity of the Lyman-α emission is proportional to the star formation rate of galaxies in Illustris, yielding a sufficiently large sample of LAEs to measure the anisotropic selection bias. We find little correlations between large-scale environment and the observed fraction induced by the RT, and hence a smaller anisotropic selection bias than what was claimed by Zheng et al. (2011). We argue that the anisotropy was overestimated in the previous work due to the insufficient spatial resolution: it is important to keep the resolution such that it resolves the high density region down to the scale of the interstellar medium, ∼1 physical kpc. (abridged)