Practical Threshold Signatures
I am not too familiar with this paper, but there is (at least) the following reason. They define $\Delta = l!$, then require (right after equation 6) that $1 = \mathsf{gcd}(e', e) = \mathsf{gcd}(4\Delta^2, e) = \mathsf{gcd}(4(l!)^2, e)$.
This is not possible if $e \leq l$ (as then the GCD is $e\neq 1$).