  An important class of three-manifolds are L-spaces, which are rational
homology spheres with the smallest possible Floer homology. For knots with an
instanton L-space surgery, we compute the framed instanton Floer homology of
all integral surgeries. As a consequence, if a knot has a Heegaard Floer and
instanton Floer L-space surgery, then the theories agree for all integral
surgeries. In order to prove the main result, we prove that the Baldwin-Sivek
contact invariant in framed instanton Floer homology is homogeneous with
respect to the absolute $\mathbb{Z}/2$-grading, but not the
$\mathbb{Z}/4$-grading.
