I do not believe the Longobards had either the numbers nor the organization (or ultimately the interest) in conquering Sicily.
The Longobard invasion was successful mostly because it came after the ravages of the long Gothic wars, followed by the Justinian plague which further depopulated Italy. The success was anyway limited, since they were able to conquer the Padan Valley at the beginning, as well as Tuscany, Spoleto and Benevento, but Liguria was much harder and dealing with the Pentapolis took them another couple of centuries almost.
Then there is the problem that they were much more backward than the Goths (who had longer to deal with both the WRE and the ERE and absorb their culture), their basic organization was the fara (an extended clan) which goes far to explain the difficulties of the string of Longobard kings in dealing with their unruly dukes and finally their Arianism was putting them in contrast with the Catholic church and the Catholic population of Italy.
While the southern duchies (Spoleto and Benevento) paid lip service to the king in Pavia, they considered themselves effectively independent (the division between Langobardia major - Padan valley and Tuscany - and Langobardia Minor (Spoleto and Benevento) started immediately, and the string of ERE fortresses and walled cities linking the Exarchate in Ravenna with the Roman Duchy did not help at all. Incidentally, the duchy of Friuli was territorially part of Langobardia major, but it was equally difficult to manage, as were more or less all the other northern duchies: the writ of the king in Pavia could not be enforced easily, even when a strong king got the throne.
The complete lack of naval culture (even before the lack of any kind of navy) would have required for them to get the help of the coastal Italian cities, none of which had the incentive to do so even if the Longobards had thought to ask (which they did not).
It is interesting to note that the duchy of Benevento was quite a powerful entity in its own (and lasted far longer than the Longobard kingdom itself), but even the dukes of Benevento never managed to conquer the coastal cities of Puglia or Campania, even after the ERE effectively abandoned any real attempt to support Naples, Gaeta and the other coastal cities of Campania.
I could swear that the idea of conquering Sicily never crossed the mind of any Longobard ruler, either in Pavia or in Benevento, and this assume that they knew where Sicily was located and why it would have been a worthwhile addiction to the kingdom (which I doubt): the king in Pavia had his own troubles (Exarchate, Pentapolis, Roman Duchy, but also unruly duchies and possible invasions both from the east and the west) which kept him extremely busy and left no time for flights of fancy.