  From the assumption that the slow roll parameter $\epsilon$ has a Lorentzian
form as a function of the e-folds number $N$, a successful model of a
quintessential inflation is obtained, as succinctly studied in
\cite{Benisty:2020xqm}. The form corresponds to the vacuum energy both in the
inflationary and in the dark energy epochs and satisfies the condition to climb
from small values of $\epsilon$ to $1$ at the end of the inflationary epoch. We
find the corresponding scalar Quintessential Inflationary potential with two
flat regions. Moreover, a reheating mechanism is suggested with numerical
estimation for the homogeneous evolution of the universe. The suggested
mechanism is consistent with the BBN bound.
