With more than 100 fb−1 recorded during LHC run 2 (2016-2018), the joint CMS-TOTEM Precision Proton Spectrometer (CT-PPS) has started to deliver its first physics results. Located between 200 and 220 m on each side from the CMS detector, it aims at detecting forward scattered protons emerging intact from the interaction, as for instance in central exclusive processes (CEP). In this paper we describe in detail the search for two-photon production of a lepton pair performed with the first 10 fb−1. This result proves the feasibility of operating near-beam detectors at the LHC under standard, high luminosity conditions. In addition, we describe the potential of PPS for future physics studies. © Owned by the author(s) under the terms of the Crea...