We present the discovery of HLock01-LAB, a luminous and large Lya nebula at z=3.326. Medium-band imaging and long-slit spectroscopic observations with the Gran Telescopio Canarias reveal extended emission in the Lya 1215AA, CIV1550AA, and HeII 1640AA lines over ~100kpc, and a total luminosity L(Lya)=(6.4+/-0.1)x10^44 erg s^-1. HLock01-LAB presents an elongated morphology aligned with two faint radio sources contained within the central ~8kpc of the nebula. The radio structures are consistent to be faint radio jets or lobes of a central galaxy, whose spectrum shows nebular emission characteristic of a type-II active galactic nucleus (AGN). The continuum emission of the AGN at short wavelengths is, however, likely dominated by stellar emission of the host galaxy, for which we derive a stellar mass M* = 2.3x10^11 Msun. The detection of extended emission in CIV and CIII] indicates that the gas within the nebula is not primordial. Feedback may have enriched the halo at at least 50 kpc from the nuclear region. Using rest-frame UV emission-line diagnostics, we find that the gas in the nebula is likely heated by the AGN. Nevertheless, at the center of the nebula we find extreme emission line ratios of Lya/CIV~60 and Lya/HeII~80, one of the highest values measured to date, and well above the standard values of photoionization models (Lya/HeII~30 for case B photoionization). Our data suggest that jet-induced shocks are likely responsible for the increase of the electron temperature and, thus, the observed Lya enhancement in the center of the nebula. This scenario is further supported by the presence of radio structures and perturbed kinematics in this region. The large Lya luminosity in HLock01-LAB is likely due to a combination of AGN photoionization and jet-induced shocks, highlighting the diversity of sources of energy powering Lya nebulae. [abridged]
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