Is ulula (an owl of some kind) a diminutive? It looks like one, but I'm not familiar with a Latin word looking remotely like ula. The word appears to be onomatopoetic to some extent, but it's hard to judge whether this is the whole story. For example, ulula might be "a little thing that says 'ula'". The entry in L&S lists some cognates, and they make me suspect that the diminutive or reduplication is a Latin (and Greek?) invention. What do we know about the etymology of ulula, especially concerning diminutives? There are some related words (eg. ululare and ululamen), but they all seem to be derived from ulula.
No, the form is accidental. Instead it's onomatopoeic, which can be deduced by it's cognates in:
Greek ololyzein [ὀλολύζειν], Sanskrit ululih "a howling," Lithuanian uluti "howl," Gaelic uileliugh "wail of lamentation," Old English ule "owl".
Greek diminutives aren't formed by a lambda. That Latin's diminutives do is coincidence.
Ululatus - defined in "The new college Latin and English Dictionary" as howling (of dogs and wolves), wailing(mourning), war cry. 2. Howl out, howl at, wail. To me since ulula -ae is owl, I assume a more accurate definition would be night howls. The root and words built on it appear to be mainly for creatures that howl, wail, or cry after dark. To answer more specifically your question, my hypothesis would be that ulula is the diminutive of ululatus, the most commonly and regularly heard creature of the night. I've not generally seen this word used for mourning, only referring to a nocturnal activity.