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Two species of mutually interacting ultracold bosonic atoms are studied in a ring-shaped trap with a species-selective azimuthal lattice which may rotate. We examine the spectrum and the states in a collective spin formalism. The system can be modeled as a pair of coupled Lipkin-Meshkov-Glick Hamiltonians, and can be used to generate a high degree of entanglement. The Hamiltonian has two components: a linear part that can be controlled by manipulating the azimuthal lattice, and an interaction-dependent quadratic part. Exact solutions are found for the quadratic part for equal strengths of intraspecies and interspecies interactions. In different regimes the Hamiltonian can emulate a beam splitter or a two-mode squeezer of quantum optical systems. We study entanglement properties of the ground state of the Hamiltonian in dependence on various parameters with the prospect of possible quantum information and metrology applications.