  We establish large-scale interior Lipschitz estimates for solutions to
systems of linear elasticity with rapidly oscillating periodic coefficients and
Dirichlet boundary conditions in domains with periodically placed inclusions of
size $\mathcal{O}(\varepsilon)$ and magnitude $\delta$ by establishing
$H^1$-convergence rates for such solutions. The interior estimates at the
macroscopic scale are derived directly without the use of compactness via a
Campanato-type scheme presented by S. Armstrong and C.K. Smart and that was
adapted for uniformly elliptic equations in by Armstrong and Z. Shen.
