This work reports the three-band structure associated with a Lieb lattice with arbitrary
nearest and next-nearest neighbors hopping interactions. For specific configurations,
the system admits a flat band located between two dispersion bands, where three inequivalent
Dirac valleys are identified. Furthermore, quasi-particles are effectively described
by a spin-1 Dirac-type equation. Under external homogeneous magnetic fields, the Landau
levels are exactly determined as the third-order polynomial equation for the energy
can be solved using Cardano's formula. It is also shown that an external anti-symmetric
field promotes the existence of current-carrying states, so-called snake states, confined
at the interface where the external field changes its sign.