Answer:
The maintainance of the lytic and the lysogenic cycle is done by the Cro and the lambda repressor proteins when the number of bacteria is higher than the number of viruses that is the mode of infectivity or MOI the virus under goes the lytic cycle. This is done by the cleaving of the proteins.
So high nutrient concentration in the gut promotes the growth of the E coli that forms a protease that cleaves the Cro protein and causes the activation of the lysis in the bacteria. So in the high nutrient concentration the bacteria is itself responsible for its lysis.