Long non-coding RNA plays a vital role in changing the expression profiles of various target genes that leads to cancer development. Thus, identifying prognostic lncRNAs related to different cancers might help in developing cancer therapy. To discover the critical lncRNAs that can identify the origin of different cancers, we proposed to use the state-of-the-art deep learning algorithm Concreate Autoencoder (CAE) in an unsupervised setting, which efficiently identifies a subset of the most informative features. However, CAE does not identify reproducible features in different runs due to its stochastic nature. We proposed a multi-run CAE (mrCAE) to identify a stable set of features to address this issue. The assumption is that a feature appearing in multiple runs carries more meaningful information about the data under consideration. The genome-wide lncRNA expression profiles of 12 different types of cancers, a total of 4,768 samples available in The Cancer Genome Atlas (TCGA), were analyzed to discover the key lncRNAs. The lncRNAs identified by multiple runs of CAE were added to the final list of key lncRNAs, which are capable of identifying 12 different cancers. Our results showed that mrCAE performs better in feature selection than single-run CAE, standard autoencoder (AE), and other state-of-the-art feature selection techniques. This study discovered a set of top-ranking 128 lncRNAs that could identify the origin of 12 different cancers with an accuracy of 95%. Survival analysis showed that 76 of 128 lncRNAs have the prognostic capability in differentiating high- and low-risk groups of patients in different cancers. The proposed mrCAE outperformed the standard autoencoder, which selects the latent features and is thought to be the upper limit in dimension reduction. Since the proposed mrCAE selects actual features and outperformed AE, it has the potential to provide information that can be used for precision medicine, such as identifying prognostic lncRNAs (this work) and mRNAs, miRNAs, and DNA methylated genes (future work) for different cancers.