We give a reformulation of the recent results of Candelas et al., Lines on the Dwork pencil of quintic threefolds, describing pencils of lines on the quintic threefold $$ \{ (x_1 : \dots : x_5) \in \mathbb{P}^4 (\mathbb{C}) \ {} \vert \ {} x^5_1 + \dots + x^5_5 = 5{\psi}x_1 \dots x_5 \} $$ in terms of the moduli space $M_{0,5}$ of curves of genus $0$ with $5$ marked points, and a generalization to pencils of lines on the degree $n$ hypersurfaces $$ \{ (x_1 : \dots : x_n) \in \mathbb{P}^{n-1} (\mathbb{C}) \ {} \vert \ {} x^n_1 + \dots + x^n_n = n{\psi}x_1 \dots x_n \} $$ in $\mathbb{P}^{n−1}(\mathbb{C})$ in terms of the moduli space $M_{0,n}$ for any odd integer $n \geq 5$.