  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 1215\AA,
CIV1550\AA, and HeII 1640\AA 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]
