  Investigations on possible violation of Lorentz invariance have been widely
pursued in the last decades, both from theoretical and experimental sides. A
comprehensive framework to formulate the problem is the standard model
extension (SME) proposed by A.Kostelecky, where violation of Lorentz invariance
is encoded into specific coefficients. Here we present a procedure to link the
deformation parameter $\beta$ of the generalized uncertainty principle (GUP) to
the SME coefficients of the gravity sector. The idea is to compute the Hawking
temperature of a black hole in two different ways. The first way involves the
deformation parameter $\beta$, and therefore we get a deformed Hawking
temperature containing the parameter $\beta$. The second way involves a
deformed Schwarzschild metric containing the Lorentz violating terms
$\bar{s}^{\mu\nu}$ of the gravity sector of the SME. The comparison between the
two different techniques yields a relation between $\beta$ and
$\bar{s}^{\mu\nu}$. In this way bounds on $\beta$ transferred from
$\bar{s}^{\mu\nu}$ are improved by many orders of magnitude when compared with
those derived in other gravitational frameworks. Also the opposite possibility
of bounds transferred from $\beta$ to $\bar{s}^{\mu\nu}$ is briefly discussed.
