The verb 'to lucubrate', along with the derived noun lucubration (commonly in the plural lucubrations), means literally and etymologically 'to burn the midnight oil' - 'to work (read and write) by artificial light, or long into the night'.
In modern times, the words (and particularly lucubrations) are more figuratively used to mean 'to produce deep and complex academic or literary work by a process of hard work'. This is often used, particularly by academics, tongue-in-cheek, ironically or to amuse.
In all the words, the pronunciation preferred in RP has a pure '-oo-' (IPA: / u:/) realization of the first vowel, reflecting the Latin derivation from lux (genitive lucis) 'light'; and the less pure 'you' (/jʊ/ in the second. In the nineteenth century it was more commonly the less pure 'you' for both. (It has never properly been the short '-u-' of 'luck', 'but' and 'cup' in either.) In the verb, the stress is on the first syllable ('LOOK-you-brate', /'lu: kjʊ breɪt/), while in the noun it falls on the third: 'look-you-BRAY-shun', /,lu: kjʊ 'breɪ ʃən/.