  We present a fully-integrated lattice Boltzmann (LB) method for
fluid--structure interaction (FSI) simulations that efficiently models
deformable solids in complex suspensions and active systems. Our Eulerian
method (LBRMT) couples finite-strain solids to the LB fluid on the same fixed
computational grid with the reference map technique (RMT). An integral part of
the LBRMT is a new LB boundary condition for moving deformable interfaces
across different densities. With this fully Eulerian solid--fluid coupling, the
LBRMT is well-suited for parallelization and simulating multi-body contact
without remeshing or extra meshes. We validate its accuracy via a benchmark of
a deformable solid in a lid-driven cavity, then showcase its versatility
through examples of soft solids rotating and settling. With simulations of
complex suspensions mixing, we highlight potentials of the LBRMT for studying
collective behavior in soft matter and biofluid dynamics.
