We present ultra-violet to mid-infrared observations of the long-lasting Type IIn supernova (SN) 2013L obtained by the Carnegie Supernova Project II (CSP-II). The spectra of SN 2013L are dominated by H emission features characterized by three components attributed to different regions. A unique feature of this Type IIn SN is that the blue shifted line profile is dominated by the macroscopic velocity of the expanding shock wave of the SN. We are therefore able to trace the evolution of the shock velocity in the dense and partially opaque circumstellar medium (CSM), from $sim 4800~km~s^{-1}$ at +48 d, decreasing as $t^{-0.23}$ to $sim 2700~km~s^{-1}$ after a year. We perform spectral modeling of both the broad- and intermediate-velocity components of the H$alpha$ line profile. The high-velocity component is consistent with emission from a radially thin, spherical shell located behind the expanding shock with emission wings broadened by electron scattering. We propose that the intermediate component originates from pre-ionized gas from the unshocked dense CSM with the same velocity as the narrow component, $sim 100~km~s^{-1}$, but also broadened by electron scattering. The spectral energy distributions (SEDs) of SN 2013L after +132 d are well reproduced by a two-component black-body (BB) model. The circumstellar-interaction model of the bolometric light curve reveals a mass-loss rate history with large values ($1.7times 10^{-2} - 0.15~M_odot~yr^{-1}$) over the $sim $25 - 40 years before explosion. The drop in the light curve at $sim 350$ days and presence of electron scattering wings at late epochs indicate an anisotropic CSM. The mass-loss rate values and the unshocked CSM velocity are consistent with the characteristics of a massive star, such as a luminous blue variable (LBV) undergoing strong eruptions, similar to $eta$ Carina.
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