  The loop-erased random walk (LERW) in $\mathbb{Z}^4$ is the process obtained
by erasing loops chronologically for simple random walk. We prove that the
escape probability of the LERW renormalized by $(\log n)^{\frac{1}{3}}$
converges almost surely and in $L^{p}$ for all $p>0$. Along the way, we extend
previous results by the first author building on slowly recurrent sets. We
provide two applications for the escape probability. We construct the two-sided
LERW, and we construct a $\pm 1$ spin model coupled with the wired spanning
forests on $\mathbb{Z}^4$ with the bi-Laplacian Gaussian field on
$\mathbb{R}^{4}$ as its scaling limit.
