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For a simple connected graph $G$ of order $n$ having distance Laplacian eigenvalues ${\rho }_1^L\ge {\rho }_2^L\ge \cdots \ge {\rho }_n^L$, the distance Laplacian energy $\mathrm{DLE}\left(G\right)$ is defined as $\mathrm{DLE}\left(G\right)={\sum }_{i=1}^n|{\rho }_i^L-2W\left(G\right)/n|$, where $W\left(G\right)$ is the Wiener index of $G$. We obtain a relationship between the Laplacian energy and the distance Laplacian energy for graphs with diameter 2. We obtain lower bounds for the distance Laplacian energy $\mathrm{DLE}\left(G\right)$ in terms of the order $n$, the Wiener index $W\left(G\right)$, the independence number, the vertex connectivity number and other given parameters. We characterize the extremal graphs...