  We have derived a non-abelian analog for the two-dimensional discrete Toda
lattice which possesses solutions in terms of quasideterminants and admits Lax
pairs of different forms. Its connection with non-abelian analogs for several
well-known (1+1) and one-dimensional lattices is discussed. In particular, we
consider a non-commutative analog of the scheme: discrete Toda equations
$\rightarrow$ Somos-$N$ sequences $\rightarrow$ discrete Painlev\'e equations.
