Continuity of Norm of Regular Representations on Étale Groupoids

Question

Let $\mathcal G$ be a locally compact, Hausdorff, étale groupoid. Following the notation found in Sims' notes (see here), for $x\in\mathcal G^{(0)}$, let $\lambda_x:C_c(\mathcal G)\to\mathbb B(\ell^2(\mathcal G_x))$ denote the regular representation: $\lambda_x(f)\xi(\gamma)=\sum_{\sigma\in\mathcal G_x}f(\gamma\sigma^{-1})\xi(\sigma)$. My question is: For fixed $f\in C_c(\mathcal G)$, is the map $$\mathcal G^{(0)}\to[0,\infty),\qquad x\mapsto\|\lambda_x(f)\|_{\mathbb B(\ell^2(\mathcal G_x))}$$ continuous, or perhaps just lower semi-continuous? I'm able to show continuity under the assumption that $f$ is supported in a bisection, however I am unable to generalize the proof to arbitrary $f\in C_c(\mathcal G)$.