  We study the de Haas-van Alphen (dHvA) oscillations in the two-dimensional
compensated metal with overtilted Dirac cones near the Lifshitz transition. We
employ the tight-binding model of $\alpha$-(BEDT-TTF)$_2$I$_3$, in which the
massless Dirac fermions are realized. When a uniaxial pressure $(P)$ along the
$y$-axis is applied above $P\simeq 0.2$ kbar in $\alpha$-(BEDT-TTF)$_2$I$_3$,
one electron pocket, which encloses the overtilted Dirac points, is changed to
two electron pockets, i.e., Lifshitz transition happens, while a hole pocket
does not change a topology. We show that the Fourier components corresponding
to the $3/2$ and $5/2$ areas of the hole pocket are anomalously enhanced in the
region of pressure where the Lifshitz transition occurs. This phenomenon will
be observed in the two-dimensional overtilted Dirac fermions near the Lifshitz
transition.
