Lateral gene transfer (LGT) has been reported in multiple eukaryotes. This process seems particularly widespread in the grass family, although we know very little about the underlying dynamics and how it impacts gene content variation within a species. Alloteropsis semialata is a tropical grass, and multiple LGT were detected in a reference genome assembled from an Australian individual. As part of this study we assemble three additional de novo genomes for A. semialata and one for its sister species Alloteropsis angusta. In total we detect 168 LGT across the five reference genomes. Using whole-genome resequencing data for a further 40 individuals we establish the distribution of these transfers and map their origin along the species phylogeny. This shows that many LGTs were acquired relatively recently, with numerous secondary losses. Exponential decay models indicate that the rate of LGT acquisitions varied significantly among lineages [6-28 per Ma], with a high rate of subsequent LGT losses [11-24% per Ma] that largely exceeds that of native loci [0.02-0.8% per Ma]. This high turnover creates large intraspecific structural variants, with a preponderance of LGT occurring as accessory genes in the Alloteropsis pangenome. The acquired genes represent unparalleled genetic novelties, having independently evolved for tens of millions of years before they were transferred. Ultimately, the rapid LGT turnover generates standing variation that can fuel local adaptation.