  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. Three inequivalent Dirac valleys are identified so that the
quasi-particles are effectively described by the 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.
