  We introduce a factorization formula for semi-leptonic $b \to u$ transitions
in the exclusive decay mode $B^- \to \pi^+\pi^-\ell^-\bar\nu_\ell$ in the limit
of large pion energies and large dipion invariant mass. One contribution can be
described in terms of a universal $B \to \pi$ form factor and the convolution
of a short-distance kernel $T^{\rm I}$ with the respective light-cone
distribution amplitudes (LCDAs) of the positively charged pion. The second
contribution, at leading power, completely factorizes, with a short-distance
kernel $T^{\rm II}$ convoluted with the leading-twist LCDAs for both pions and
the $B$-meson. We calculate the leading contributions to the short-distance
kernels $T^{\rm I}$ and $T^{\rm II}$ in fixed-order perturbation theory, and
discuss the approximate relations among the resulting $B \to \pi\pi$
partial-wave form factors. Our results provide useful theoretical constraints
for phenomenological models that aim to analyze the complete $B \to \pi\pi
\ell\nu$ phase space.
