  We consider a model where massive static spherically symmetric black hole, in
the presence of power-Yang-Mills source, is surrounded by a dark fluid with
non-linear equation of state. In this set up we construct a new class of
magnetized Lovelock black hole solutions of the gravitational field equations.
In particular, we work out the metric functions in both D-dimensional massive
Einstein and massive Gauss-Bonnet gravities. We study thermodynamics of these
black holes also and show that the mass and associated thermodynamic quantities
like Hawking temperature and heat capacity depend on parameters of the dark
fluid and the power-Yang-Mills magnetic source. We note that the entropy does
not satisfy the area law in Gauss-Bonnet and higher order Lovelock black holes.
Furthermore, phase transitions of black holes in each case are also discussed.
