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Evidence has been emerging of the importance of long non‐coding RNAs (lncRNAs) in genome instability. However, no study has established how to classify such lncRNAs linked to genomic instability, and whether that connection poses a therapeutic significance. Here, we established a computational frame derived from mutator hypothesis by combining profiles of lncRNA expression and those of somatic mutations in a tumor genome, and identified 185 candidate lncRNAs associated with genomic instability in lung adenocarcinoma (LUAD). Through further studies, we established a six lncRNA‐based signature, which assigned patients to the high‐ and low‐risk groups with different prognosis. Further validation of this signature was performed in a number of separate cohorts of LUAD patients. In addition, the signature was found closely linked to genomic mutation rates in patients, indicating it could be a useful way to quantify genomic instability. In summary, this research offered a novel method by through which more studies may explore the function of lncRNAs and presented a possible new way for detecting biomarkers associated with genomic instability in cancers. [ABSTRACT FROM AUTHOR]