  In this note we discuss the conditional stability issue for the finite
dimensional Calder\'on problem for the fractional Schr\"{o}dinger equation with
a finite number of measurements. More precisely, we assume that the unknown
potential $q \in L^{\infty}(\Omega) $ in the equation $((-\Delta)^s+ q)u = 0
\mbox{ in } \Omega\subset \mathbb{R}^n$ satisfies the a priori assumption that
it is contained in a finite dimensional subspace of $L^{\infty}(\Omega)$. Under
this condition we prove Lipschitz stability estimates for the fractional
Calder\'on problem by means of finitely many Cauchy data depending on $q$. We
allow for the possibility of zero being a Dirichlet eigenvalue of the
associated fractional Schr\"odinger equation. Our result relies on the strong
Runge approximation property of the fractional Schr\"odinger equation.
