We consider a system of three particles consisting of two identical fermions and one other particle on a one-dimensional lattice. The fermions interact via a nearest-neighbor potential of strength
μ1∈R , while the interaction between a fermion and one other particle is via an on-site potential with strength
μ2∈R . We establish existence of bound states of the associated three-body lattice Schrödinger operator for all values of the total quasimomentum
K∈T1 . Furthermore, we show that both the bound state
fμ1μ2(K;⋅,⋅) and its corresponding eigenvalue
Eμ1μ2(K) depend holomorphically on the quasimomentum.