Functional redundancy in genomes arises from genes with overlapping functions, allowing phenotypes to persist after gene knockouts. Evolutionary redundancy or evolvability of a genome is one step removed, in that functional redundancy is absent but the genome has the potential to evolve to restore a lost phenotype. Exploring the extent to which this recovery alters gene networks can illuminate how functional gene interactions change through time. Here, the evolvability of lysis was studied in bacteriophage T7, revealing hidden functional interactions. Lysis is the destruction of host cell wall and membranes that releases progeny and is therefore essential for phage propagation. In most phages, lysis is mediated by a two-component genetic module: a muralytic enzyme that degrades the bacterial cell wall (endolysin) and a holin that permeabilizes the inner membrane to allow the endolysin access to the cell wall. T7 carries one known holin, one endolysin, and a second muralytic enzyme that plays little role in lysis by wild-type phage. If the primary endolysin is deleted, the second muralytic enzyme evolves to restore normal lysis after selection for faster growth. Here, a second level of evolutionary redundancy was revealed. When the second muralytic enzyme was prevented from adapting in a genome lacking the primary endolysin, the phage reevolved lysis de novo in the absence of any known muralytic enzymes by changes in multiple genes outside the original lysis module. This second level of redundancy proved to be evolutionarily inferior to the first, and both result in a lower fitness and slower lysis than wild-type T7. Deletion of the holin gene delayed lysis time modestly; fitness was restored by compensatory substitutions in genes that lack known roles in lysis of the wild type.