  We provide an extension of the Gravitational Decoupling (algorithm) for the
Lovelock theory with Unique Vacuum (LUV), which represents a simple way to
solve the equations of motion. Due to the application of this algorithm, the
energy of the system splits in the {\it energy of the seed solution} and the
{\it energy of each quasi-LUV sector}. Under certain assumptions imposed, the
total energy varies due to the contribution of energy of each quasi-LUV sector.
It is provided a new solution, whose energy differs from the energy of the seed
solution in a quantity that depends on the number of extra sources. The new
solution has two inner horizons, which is a proper characteristic of itself.
Furthermore, its thermodynamics differs from the seed solution, since our
solution is always stable and does not have phase transitions. Since the first
law of thermodynamics is modified by the presence of the matter fields, we
provide a new version of the first law for LUV, where a local definition of the
variation of energy is defined, and, where the entropy and temperature are
consistent for LUV theory.
