Isn't a word. Sorry.
Are you sure about it? I am not a native speaker but when I search "drawerful" with google, I get several results decribing it exactly the way I expected. Is the information provided on these websites wrong, or is it just not used that much? But it is a word that came to my mind without using dictionaries.
Anyway, for the case that it is a word, I am not sure if it sounds close enough to count as rhyming to "lawful".