  To any lattice $L \subset \mathbb{Z}^{m}$ one can associate the lattice ideal
$I_{L} \subset K[x_{1},...,x_{m}]$. This paper concerns the study of the
relation between the binomial arithmetical rank and the minimal number of
generators of $I_{L}$. We provide lower bounds for the binomial arithmetical
rank and the $\mathcal{A}$-homogeneous arithmetical rank of $I_{L}$.
Furthermore, in certain cases we show that the binomial arithmetical rank
equals the minimal number of generators of $I_{L}$. Finally we consider a class
of determinantal lattice ideals and study some algebraic properties of them.
