If $\Gamma\subseteq SL(n,\mathbb{R})$ is a lattice (i.e. discrete and finite covolume), does $\Gamma$ necessarily contain some $\mathbb{R}$-diagonalizable copy of $\mathbb{Z}^{n-1}$?

I know that the answer is yes if the lattice is cocompact, and that the answer is also yes in the case $\Gamma=SL(n,\mathbb Z)$. So I wonder if every lattice satisfies this property.