Chemistry 9th Edition

The hydration of $Al(OH)_3$ is not energetically favorable enough to overcome the comparatively more energetically unfavorable process of breaking the lattice while the hydration of $NaOH$is energetically favorable enough to overcome the comparatively less energetically unfavorable process of breaking the lattice.
$Al(OH)_3$ has a much stronger lattice energy than $NaOH$ because lattice energy is directly proportional to the ion charge, and the charge of the ions in $Al(OH)_3$ is 3 while the charge of the ions in $NaOH$ is 1.