In bacteria, the key mechanism governing mutation, adaptation and survival upon DNA damage is the SOS response. Through autoproteolytic digestion triggered by single-stranded DNA caused by most antibiotics, the transcriptional repressor LexA controls over 50 SOS genes including DNA repair pathways and drivers of mutagenesis. Efforts to inhibit this response and thereby combat antibiotic resistance rely on a broad understanding of its behavior in vivo, which is still limited. Here, we develop a single-molecule localization microscopy assay to directly visualize LexA mobility in Escherichia coli and monitor the SOS response on the level of transcription factor activity. We identify four diffusive populations and monitor their temporal evolution upon ciprofloxacin-induced continuous DNA damage. With LexA mutants, we assign target bound, non-specifically DNA bound, freely diffusing and cleaved repressors. We develop a strategy to count LexA in fixed cells at different time points after antibiotic stress and combine the time-evolution of LexA sub-populations and the repressor's overall abundance. Through fitting a detailed kinetic model we obtain in vivo synthesis, cleavage and binding rates and determined that the regulatory feedback system reaches a new equilibrium in ~100 min. LexA concentrations showed non-constant heterogeneity during SOS response and designate LexA expression, and thereby regulation of downstream SOS proteins, as drivers of evolutionary adaptation. Even under low antibiotic stress, we observed a strong SOS response on the LexA level, suggestion that small amounts of antibiotics can trigger adaptation in E. coli.