Let $(Y_1,\dots,Y_n)$ have a joint $n$-dimensional Gaussian distribution with a general mean vector and a general covariance matrix, and let $X_i=\e^{Y_i}$, $S_n=$ $X_1+\dots+X_n$. The asymptotics of $\mathbb{P}(S_n>x)$ as $n\to\infty$ is shown to be the same as for the independent case with the same lognormal marginals. Further, a number of simulation algorithms based on conditional Monte Carlo ideas are suggested and their efficiency properties studied.