  In the recent paper arXiv:1807.02721, B. Lawrence and A. Venkatesh develop a
method of proving finiteness theorems in arithmetic geometry by studying the
geometry of families over a base variety. Their results include a new proof of
both the $S$-unit theorem and Faltings' theorem, obtained by constructing and
studying suitable abelian-by-finite families over
$\mathbb{P}^1\setminus\{0,1,\infty\}$ and over an arbitrary curve of genus
$\geq 2$ respectively. In this paper, we apply this strategy to reprove
Siegel's theorem: we construct an abelian-by-finite family on a punctured
elliptic curve to prove finiteness of $S$-integral points on elliptic curves.
