  The random walk loop soup is a Poissonian ensemble of lattice loops; it has
been extensively studied because of its connections to the discrete Gaussian
free field, but was originally introduced by Lawler and Trujillo Ferreras as a
discrete version of the Brownian loop soup of Lawler and Werner, a conformally
invariant Poissonian ensemble of planar loops with deep connections to
conformal loop ensembles (CLEs) and the Schramm-Loewner evolution (SLE).
  Lawler and Trujillo Ferreras showed that, roughly speaking, in the continuum
scaling limit, ``large'' lattice loops from the random walk loop soup converge
to ``large'' loops from the Brownian loop soup. Their results, however, do not
extend to clusters of loops, which are interesting because the connection
between Brownian loop soup and CLE goes via cluster boundaries. In this paper,
we study the scaling limit of clusters of ``large'' lattice loops, showing that
they converge to Brownian loop soup clusters. In particular, our results imply
that the collection of outer boundaries of outermost clusters composed of
``large'' lattice loops converges to CLE.
