  We investigate the ground state properties of a lattice trapped bosonic
system coupled to a Lieb-Liniger type gas. Our main goal is the description and
in depth exploration and analysis of the two-species many-body quantum system
including all relevant correlations beyond the standard mean-field approach. To
achieve this, we use the Multi-Configuration Time-Dependent Hartree method for
Mixtures (ML-MCTDHX). Increasing the lattice depth and the interspecies
interaction strength, the wave function undergoes a transition from an
uncorrelated to a highly correlated state, which manifests itself in the
localization of the lattice atoms in the latter regime. For small interspecies
couplings, we identify the process responsible for this cross-over in a
single-particle-like picture. Moreover, we give a full characterization of the
wave function's structure in both regimes, using Bloch and Wannier states of
the lowest band, and we find an order parameter, which can be exploited as a
corresponding experimental signature. To deepen the understanding, we use an
effective Hamiltonian approach, which introduces an induced interaction and is
valid for small interspecies interaction. We finally compare the ansatz of the
effective Hamiltonian with the results of the ML-MCTDHX simulations.
