Long noncoding RNAs (lncRNAs) are linked to cancer via pathogenic changes in their expression levels. Yet, it remains unclear whether lncRNAs can also impact tumour cell fitness via function-altering somatic "driver" mutations. To search for such driver-lncRNAs, we here perform a genome-wide analysis of fitness-altering single nucleotide variants (SNVs) across a cohort of 2583 primary and 3527 metastatic tumours. The resulting 54 mutated and positively-selected lncRNAs are significantly enriched for previously-reported cancer genes and a range of clinical and genomic features. A number of these lncRNAs promote tumour cell proliferation when overexpressed in in vitro models. Our results also highlight a dense SNV hotspot in the widely-studied NEAT1 oncogene. To directly evaluate the functional significance of NEAT1 SNVs, we use in cellulo mutagenesis to introduce tumour-like mutations in the gene and observe a significant and reproducible increase in cell fitness, both in vitro and in a mouse model. Mechanistic studies reveal that SNVs remodel the NEAT1 ribonucleoprotein and boost subnuclear paraspeckles. In summary, this work demonstrates the utility of driver analysis for mapping cancer-promoting lncRNAs, and provides experimental evidence that somatic mutations can act through lncRNAs to enhance pathological cancer cell fitness.