Extensive tracts of the mammalian genome that lack protein-coding function are still transcribed into long noncoding RNA. While these lncRNAs are generally short lived, length restricted, and non-polyadenylated, how their expression is distinguished from protein-coding genes remains enigmatic. Surprisingly, depletion of the ubiquitous Pol-II-associated transcription elongation factor SPT6 promotes a redistribution of H3K36me3 histone marks from active protein coding to lncRNA genes, which correlates with increased lncRNA transcription. SPT6 knockdown also impairs the recruitment of the Integrator complex to chromatin, which results in a transcriptional termination defect for lncRNA genes. This leads to the formation of extended, polyadenylated lncRNAs that are both chromatin restricted and form increased levels of RNA:DNA hybrid (R-loops) that are associated with DNA damage. Additionally, these deregulated lncRNAs overlap with DNA replication origins leading to localized DNA replication stress and a cellular senescence phenotype. Overall, our results underline the importance of restricting lncRNA expression.