  Given any $d$-dimensional Lipschitz Riemannian manifold $(M,g)$ with heat
kernel $\mathsf{p}$, we establish uniform upper bounds on $\mathsf{p}$ which
can always be decoupled in space and time. More precisely, we prove the
existence of a constant $C>0$ and a bounded Lipschitz function $R\colon M \to
(0,\infty)$ such that for every $x\in M$ and every $t>0$, \begin{align*}
\sup_{y\in M} \mathsf{p}(t,x,y) \leq C\min\{t, R^2(x)\}^{-d/2}. \end{align*}
This allows us to identify suitable weighted Lebesgue spaces w.r.t. the given
volume measure as subsets of the Kato class induced by $(M,g)$. In the case
$\partial M \neq \emptyset$, we also provide an analogous inclusion for
Lebesgue spaces w.r.t. the surface measure on $\partial M$.
  We use these insights to give sufficient conditions for a possibly
noncomplete Lipschitz Riemannian manifold to be tamed, i.e. to admit a
measure-valued lower bound on the Ricci curvature, formulated in a synthetic
sense.
