  A relation between semi-direct sums of Lie algebras and integrable couplings
of lattice equations is established, and a practicable way to construct
integrable couplings is further proposed. An application of the resulting
general theory to the generalized Toda spectral problem yields two classes of
integrable couplings for the generalized Toda hierarchy of lattice equations.
The construction of integrable couplings using semi-direct sums of Lie algebras
provides a good source of information on complete classification of integrable
lattice equations.
