We present the discovery of HLock01-LAB, a luminous and large Lyα nebula at z = 3.326. Medium-band imaging and long-slit spectroscopic observations with the Gran Telescopio Canarias reveal extended emission in the Lyα 1215 Å, C IV 1550 Å, and He II 1640 Å lines over ˜100 kpc, and a total luminosity LLyα = (6.4 ± 0.1)×1044 erg s-1. HLock01-LAB presents an elongated morphology aligned with two faint radio sources contained within the central ˜8 kpc of the nebula. The radio structures are consistent with 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* ≃ 2.3 × 1011 M⊙. Our kinematic analysis shows that the ionized gas is perturbed almost exclusively in the inner region between the radio structures, probably as a consequence of jet-gas interactions, whereas in the outer regions the ionized gas appears more quiescent. The detection of extended emission in C IV and C III] 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 Lyα/C IV ˜60 and Lyα/He II ˜80, one of the highest values measured to date, and well above the standard values of photoionization models (Lyα/He II ˜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 Lyα 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 Lyα 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 Lyα nebulae. Future follow-up observations of HLock01-LAB will help to reveal the finer details of the excitation conditions of the gas induced by jets and to investigate the underlying cooling and feedback processes in this unique object. The reduced images and 2D spectra are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/629/A23