We consider the problem of recovering a k-sparse signal ${\mathit{\beta }}_0\in {\mathbb{R}}^p$ from noisy observations $\mathbf{y}=\mathbf{X}{\mathit{\beta }}_0+\mathbf{w}\in {\mathbb{R}}^n$. One of the most popular approaches is the $l_1$-regularized least squares, also known as LASSO. We analyze the mean square error of LASSO in the case of random designs in which each row of X is drawn from distribution $N(0,\mathrm{\Sigma })$ with general $\mathrm{\Sigma }$. We first derive the asymptotic risk of LASSO for $\mathbf{w}\ne 0$ in the limit of $n,p\to \infty$ with $n∕p\to \mathit{\delta }\in [0,\infty )$. We then examine conditions on n, p, and k for LASSO to exactly reconstruct ${\mathit{\beta }}_0$ in the noiseless case $\mathbf{w}=0$. A phase boundary ${\mathit{\delta }}_c=\mathit{\delta }(\mathit{ϵ})$ is precisely established in the phase space defined by $0\le \mathit{\delta },\mathit{ϵ}\le 1$, where $\mathit{ϵ}=k∕p$. Above this boundary, LASSO perfectly recovers ${\mathit{\beta }}_0$ with high probability. Below this boundary, LASSO fails to recover ${\mathit{\beta }}_0$ with high probability. While the values of the non-zero elements of ${\mathit{\beta }}_0$ do not have any effect on the phase transition curve, our analysis shows that ${\mathit{\delta }}_c$ does depend on the signed pattern of the nonzero values of ${\mathit{\beta }}_0$ for general $\mathrm{\Sigma }\ne {\mathbf{I}}_{p\times p}$. This is in sharp contrast to the previous phase transition results derived in i.i.d. case with $\mathrm{\Sigma }={\mathbf{I}}_{p\times p}$ where ${\mathit{\delta }}_c$ is completely determined by ϵ regardless of the distribution of ${\mathit{\beta }}_0$. Underlying our formalism is a recently developed efficient algorithm called approximate message passing (AMP) algorithm. We generalize the state evolution of AMP from i.i.d. case to general case with $\mathrm{\Sigma }\ne {\mathbf{I}}_{p\times p}$. Extensive computational experiments confirm that our theoretical predictions are consistent with simulation results on moderate size system.