  In 1947, Lehmer conjectured that the Ramanujan \tau-function \tau(m) is
non-vanishing for all positive integers m, where \tau(m) are the Fourier
coefficients of the cusp form \Delta of weight 12. It is known that Lehmer's
conjecture can be reformulated in terms of spherical t-design, by the result of
Venkov. In this paper, we show that \tau(m) = 0 is equivalent to the fact that
the homogeneous space of the moonshine vertex operator algebra
(V^\natural)_{m+1} is a conformal 12-design. Therefore, Lehmer's conjecture is
now reformulated in terms of conformal t-designs.
