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
1215Å, CIV1550Å, and HeII 1640Ålines 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]