Long-lived particles that are present in many new physics models beyond the standard model, can be searched for in a number of newly proposed lifetime frontier experiments at the LHC. The signals of the long-lived dark photons can be significantly enhanced in a new dark photon model in which dark photons are copiously produced in the hidden radiation process. We investigate the capability of various lifetime frontier detectors in probing the parameter space of this model, including the far forward detectors FACET and FASER, the far transverse detector MATHUSLA, and the precision timing detector CMS-MTD. We find that the accessible parameter space is significantly enlarged by the hidden radiation process so that FACET, MATHUSLA, and CMS-MTD can probe a much larger parameter space than the so-called minimal model. The parameter space probed by FACET is found to be much larger than FASER, which is largely due to the fact that the former has a larger decay volume and is closer to the interaction point. There also exists some parameter space that can be probed both by the far detectors and by precision timing detectors, so that different experiments can be complementary to each other. A brief overview of the lifetime frontier detectors is also given.