This paper is devoted to proving the sharpness on the lower bound of the lifespan of classical solutions to general nonlinear wave equations with small initial data in the case n = 2 and cubic nonlinearity (see the results of T. T. Li and Y. M. Chen in 1992). For this purpose, the authors consider the following Cauchy problem: {□u=(ut)3, n=2, t=0:u=0,ut=εg(x),x∈R2, where □ = (a)2t -n∑I=1(a)2xi is the wave operator, g(x) ≠ 0 is a smooth non-negative function on R2 with compact support, and ε ＞ 0 is a small parameter. It is shown that the solution blows up in a finite time, and the lifespan T(ε) of solutions has an upper bound T(ε) ≤ exp(Aε-2) with a positive constant A independent of ε, which belongs to the same kind of the lower bound of the lifespan.