MOTIVATION: As more population genetics datasets and population-specific references become available, the task of translating ('lifting') read alignments from one reference coordinate system to another is becoming more common. Existing tools generally require a chain file, whereas VCF files are the more common way to represent variation. Existing tools also do not make effective use of threads, creating a post-alignment bottleneck. RESULTS: LevioSAM is a tool for lifting SAM/BAM alignments from one reference to another using a VCF file containing population variants. LevioSAM uses succinct data structures and scales efficiently to many threads. When run downstream of a read aligner, levioSAM is more than 7 times faster than an aligner when both are run with 16 threads. AVAILABILITY AND IMPLEMENTATION: Software Package: https://github.com/alshai/levioSAM, Experiments: https://github.com/langmead-lab/levioSAM-experiments. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.