  In this paper we provide another application of the Inhomogeneous
Hopf-Ole\u{\i}nik Lemma (IHOL) proved in \cite{BM-IHOL-PartI} or
\cite{Boyan-2}. As a matter of fact, we also provide a new and simpler proof of
a slightly weaker version IHOL for the uniformly elliptic fully nonlinear case
which is sufficient for most purposes. The paper has essentially two parts. In
the first part, we use IHOL for unbounded RHS to develop a Caffarelli's
"Lipschitz implies $C^{1,\alpha}$" approach to prove Ladyzhenskaya-Uraltseva
boundary gradient type estimates for functions in $S^{*}(\gamma, f)$ that
vanishes on the boundary. Here, unbounded RHS means that $f\in L^{q}$ with
$q>n$. This extends the celebrated Krylov's boundary gradient estimate proved
in \cite{Krylov}. A Phragm\'en-Lindel\"of classification result for solutions
in half spaces is recovered from these estimates. Moreover, a H\"older estimate
up to the boundary (in the half-ball) for $u(x)/x_{n}$ is obtained. In the
second part, we extend the previous results for functions in $S^{*}(\gamma,
\sigma, f)$ where $\gamma,f\in L^{q}$ with $q>n$ that have a $C^{1,Dini}$
boundary data on a $W^{2,q}$ domain. Here, we use an "improvement of flatness"
strategy suited to the unbounded coefficients scenario. As a consequence of
that, a quantitative version of IHOL under pointwise $C^{1,Dini}$ boundary
regularity is obtained.
