Bacteria form groups comprised of cells and a secreted polymeric matrix that controls their spatial organization. These groups - termed biofilms - can act as refuges from environmental disturbances and from biotic threats, including phages. Despite the ubiquity of temperate phages and bacterial biofilms, live propagation of temperate phages within biofilms has never been characterized on cellular spatial scales. Here, we leverage several approaches to track temperate phages and distinguish between lytic and lysogenic host infections. We determine that lysogeny within E. coli biofilms initially occurs within a predictable region of cell group packing architecture on the biofilm periphery. Because lysogens are generally found on the periphery of large cell groups, where lytic viral infections also reduce local biofilm cell packing density, lysogens are predisposed to disperse into the passing liquid and are over-represented in biofilms formed from the dispersal pool of the original biofilm-phage system. Comparing our results with those for virulent phages reveals that temperate phages have previously unknown advantages in propagating over long spatial and time scales within and among bacterial biofilms.