  There is strong observational evidence that almost every large galaxy has a
supermassive black hole at its center. It is of fundamental importance to know
whether such black holes are described by the standard Kerr solution in General
Relativity (GR) or by another black hole solution. An interesting alternative
is the so-called disformal Kerr black holes which exist within the framework of
degenerate higher-order scalar-tensor (DHOST) theories of gravity. The
departure from the standard Kerr black hole spacetime is parametrized by a
parameter $D$, called $\textit{disformal parameter}$. In the present work, we
discuss the capability of LISA to detect the disformal parameter. For this
purpose, we study Extreme Mass Ratio Inspirals (EMRI's) around disformal Kerr
black holes within the framework of the quadrupole hybrid formalism. Even when
the disformal parameter is very small, its effect on the globally accumulated
phase of the gravitational waveform of an EMRI can be significant due to the
large number of cycles in the LISA band made by the small compact object. We
show that LISA will in principle be able to detect and measure extremely small
values of the disformal parameter which in turn, can be seen as an assessment
of LISA's ability to detect very small deviations from the Kerr geometry.
