$V_{ub}$ is the smallest and least known of all CKM matrix elements; it is currently determined primarily through the exclusive process $B\to\pi\ell\bar{\nu}$, and additional channels to determine it are welcomed by the community. We will present progress toward a lattice QCD determination of $|V_{ub}|$ from the $B\to\pi\pi\ell\bar{\nu}$ process, where the $\pi\pi$ system is in a $P$-wave and features the $\rho(770)$ resonance as an enhancement. After an overview of the theoretical framework, we will discuss some preliminary results.