The critical behaviour of d-dimensional n-vector models at m-axial Lifshitz points is considered for general values of m in the large-n limit. It is proven that the recently obtained large-N expansions [J. Phys.: Condens. Matter 17, S1947 (2005)] of the correlation exponents eta_{L2}, eta_{L4} and the related anisotropy exponent theta are fully consistent with the dimensionality expansions to second order in epsilon=4+m/2-d [Phys. Rev. B 62, 12338 (2000); Nucl. Phys. B 612, 340 (2001)] inasmuch as both expansions yield the same contributions of order epsilon^2/n.
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