Many microbes can acquire genetic material from their environment and incorporate it into their genome, a process known as lateral genetic transfer (LGT). Computational approaches have been developed to detect genomic regions of lateral origin, but typically lack sensitivity, ability to distinguish donor from recipient, and scalability to very large datasets. To address these issues we have introduced an alignment-free method based on ideas from document analysis, term frequency-inverse document frequency (TF-IDF). Here we examine the performance of TF-IDF on three empirical datasets: 27 genomes of Escherichia coli and Shigella, 110 genomes of enteric bacteria, and 143 genomes across 12 bacterial and three archaeal phyla. We investigate the effect of k-mer size, gap size and delineation of groups on the inference of genomic regions of lateral origin, finding an interplay among these parameters and sequence divergence. Because TF-IDF identifies donor groups and delineates regions of lateral origin within recipient genomes, aggregating these regions by gene enables us to explore, for the first time, the mosaic nature of lateral genes including the multiplicity of biological sources, ancestry of transfer and over-writing by subsequent transfers. We carry out Gene Ontology enrichment tests to investigate which biological processes are potentially affected by LGT.