  In this paper, we study the Lagrangian F-stability of closed Lagrangian
self-shrinkers immersed in complex Euclidean space. We show that any closed
Lagrangian self-shrinker with first Betti number greater than one is Lagrangian
F-unstable. In particular, any two-dimensional embedded closed Lagrangian
self-shrinker is Lagrangian F-unstable. For a closed Lagrangian self-shrinker
with first Betti number equal to one, we show that Lagrangian F-stability is
equivalent to Hamiltonian F-stability. We also characterize Hamiltonian
F-stability of a closed Lagrangian self-shrinker by its spectral property of
the twisted Laplacian.
