We present ultra-violet ( UV ) to mid-infrared ( MIR ) observations of the long-lasting Type IIn supernova ( SN ) 2013L obtained by the Carnegie Supernova Project II ( CSP-II ) beginning two days after discovery and extending until +887 days ( d ) . The SN reached a peak r -band absolute magnitude of \approx - 19 mag and an even brighter UV peak , and its light curve evolution resembles that of SN 1988Z . The spectra of SN 2013L are dominated by hydrogen emission features , characterized by three components attributed to different emission regions . A unique feature of this Type IIn SN is that , apart from the first epochs , 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 performed 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 preionized gas from the unshocked dense CSM with the same velocity as the narrow component , \sim 100 ~ { } km~ { } s ^ { -1 } , but also that it is broadened by electron scattering . These features provide direct information about the shock structure , which is consistent with model calculations . The spectra exhibit broad O i and [ O i ] lines that emerge at \gtrsim +144 d and broad Ca ii features . The spectral continua and the spectral energy distributions ( SEDs ) of SN 2013L after +132 d are well reproduced by a two-component black-body ( BB ) model ; one component represents emitting material with a temperature between 5 \times 10 ^ { 3 } to 1.5 \times 10 ^ { 4 } K ( hot component ) and the second component is characterized by a temperature around 1–1.5 \times 10 ^ { 3 } K ( warm component ) . The warm component dominates the emission at very late epochs ( \gtrsim +400 d ) , as is evident from both the last near infrared ( NIR ) spectrum and MIR observations obtained with the Spitzer Space Telescope . Using the BB fit to the SEDs , we constructed a bolometric light curve that was modeled together with the unshocked CSM velocity and the shock velocity derived from the H \alpha line modeling . The circumstellar-interaction model of the bolometric light curve reveals a mass-loss rate history with large values ( 1.7 \times 10 ^ { -2 } -0.15 ~ { } ~ { } M _ { \odot } ~ { } yr ^ { -1 } ) over the \sim 25 – 40 years before explosion , depending on the radiative efficiency and anisotropies in the CSM . The drop in the light curve at \sim 350 days and the 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 . Our analysis also suggests a scenario where pre-existing dust grains have a distribution that is characterized by a small covering factor .