Cuproptosis is an unusual form of cell death caused by copper accumulation in mitochondria. Cuproptosis is associated with hepatocellular carcinoma (HCC). Long noncoding RNAs (LncRNAs) have been shown to be effective prognostic biomarkers, yet the link between lncRNAs and cuproptosis remains unclear. We aimed to build a prognostic model of lncRNA risk and explore potential biomarkers of cuproptosis in HCC. Pearson correlations were used to derive lncRNAs co-expressed in cuproptosis. The model was constructed using Cox, Lasso, and multivariate Cox regressions. Kaplan–Meier survival analysis, principal components analysis, receiver operating characteristic curve, and nomogram analyses were carried out for validation. Seven lncRNAs were identified as prognostic factors. A risk model was an independent prognostic predictor. Among these seven lncRNAs, prostate cancer associated transcript 6 (PCAT6) is highly expressed in different types of cancer, activating Wnt, PI3K/Akt/mTOR, and other pathways; therefore, we performed further functional validation of PCAT6 in HCC. Reverse transcription–polymerase chain reaction results showed that PCAT6 was aberrantly highly expressed in HCC cell lines (HepG2 and Hep3B) compared to LO2 (normal hepatocytes). When its expression was knocked down, cells proliferated and migrated less. PCAT6 might be a potential biomarker for predicting prognosis in HCC.