This study essentially consists of two separate investigations where we study neutron-rich isotopes of copper. Two different nuclear models were selected to perform the two investigations. In the first part of this paper, the nuclear ground-state properties of neutron-rich copper isotopes (72 <= A <= 82) have been studied with the help of the relativistic mean field (RMF) model. The second portion of this paper is dedicated to calculation of lepton capture rates in stellar environment. Ground and excited states of GT and U1F strength functions were calculated in a microscopic way employing the deformed proton-neutron quasiparticle random phase approximation (pn-QRPA) model. The lepton capture rates were computed on a wide temperature range of (0.01-30) x 10(9) K and stellar density range of (10-10(11)) g/cm(3). We compared our computed half-lives (GT + U1F) with previous theoretical and measured results. Our calculated terrestrial half-lives agree well with the measured ones. Our study shows that, at high stellar temperatures, allowed GT and, specially, U1F positron capture rates dominate the competing beta-decay rates. For a better description of presupernova evolutionary phases of massive stars, simulators are recommended to take into account lepton capture rates on neutron-rich copper isotopes presented in this work.