Recombinase enzymes are extremely efficient at integrating very large DNA fragments into target genomes. However, intrinsic sequence specificities curtail their use to DNA sequences with sufficient homology to endogenous target motifs. Extensive engineering is therefore required to broaden applicability and robustness. Here, we describe the directed evolution of novel lambda integrase variants capable of editing exogenous target sequences identified in the diatom Phaeodactylum tricornutum and the algae Nannochloropsis oceanica. These microorganisms hold great promise as conduits for green biomanufacturing and carbon sequestration. The evolved enzyme variants show >1000-fold switch in specificity towards the non-natural target sites when assayed in vitro. A single-copy target motif in the human genome with homology to the Nannochloropsis oceanica site can also be efficiently targeted using an engineered integrase, both in vitro and in human cells. The developed integrase variants represent useful additions to the DNA editing toolbox, with particular application for targeted genomic insertion of large DNA cargos.