Assuming you are referring to a lambda lysogen that carries the wild type repressor (cI) and not some mutant of cI, then the traditional methods for inducing a lysogen are adding mitomycin C (about 1ug/ml) or by UV exposure sufficient to induce the SOS system but not so high as to induce a high rate of mutagenesis or killing to wild type cells.

UV works fine for small cultures (once you have the lamps calibrated) maybe up to 10 ml or less. Mitomycin C can be used at any volume.