Determining the habitability and interpreting atmospheric spectra of exoplanets requires understanding their atmospheric physics and chemistry. We use a 3-D coupled climate-chemistry model, the Met Office Unified Model with the UK Chemistry and Aerosols framework, to study the emergence of lightning and its chemical impact on tidally-locked Earth-like exoplanets. We simulate the atmosphere of Proxima Centauri b orbiting in the Habitable Zone of its M-dwarf star, but the results apply to similar M-dwarf orbiting planets. Our chemical network includes the Chapman ozone reactions and hydrogen oxide (HO_x = H + OH + HO₂) and nitrogen oxide (NO_x = NO + NO₂) catalytic cycles. We find that photochemistry driven by stellar radiation (177–850 nm) supports a global ozone layer between 20–50 km. We parametrize lightning flashes as a function of cloud-top height and the resulting production of nitric oxide (NO) from the thermal decomposition of N₂ and O₂. Rapid dayside convection over and around the substellar point results in lightning flash rates of up to 0.16 flashes km⁻² yr⁻¹, enriching the dayside atmosphere below altitudes of 20 km in NO_x. Changes in dayside ozone are determined mainly by UV irradiance and the HO_x catalytic cycle. ∼45 per cent of the planetary dayside surface remains at habitable temperatures (T_surf > 273.15K), and the ozone layer reduces surface UV radiation levels to 15 per cent. Dayside–nightside thermal gradients result in strong winds that subsequently advect NO_x towards the nightside, where the absence of photochemistry allows NO_x chemistry to involve reservoir species. Our study also emphasizes the need for accurate UV stellar spectra to understand the atmospheric chemistry of exoplanets.