The unoccupied electronic structure of quasi-one-dimensional reconstructions of Pb atoms on a Si(557) surface is investigated by means of femtosecond time- and angle-resolved two-photon photoemission. Two distinct unoccupied electronic states are observed at E-EF=3.55 and 3.30 eV, respectively. Density functional theory calculations reveal that these states are spatially located predominantly on the lead wires and that they are energetically degenerated with an energy window of reduced electronic density of states in Si. We further find momentum-averaged lifetimes of 24 and 35 fs of these two states, respectively. The photoemission yield and the population dynamics depend on the electron momentum component perpendicular to the steps of the Si substrate, and the momentum-dependent dynamics cannot be described by means of rate equations. We conclude that momentum- and direction-dependent dephasing of the electronic excitations, likely caused by elastic scattering at the step edges on the vicinal surface, modifies the excited-state population dynamics in this system. © 2015 American Physical Society.