This is a really good question, and I'm kinda eager to hear an answer.

As a somewhat related question, was it common for mercenary armies to stick together as a cohesive force for so long?

Nothing that I have read indicates that a lingua franca developed for the entire army (and I have read quite a bit on the Second Punic War).

The Carthaginian army was organised along 'ethnic' lines, with each sub-group of the army (Numidians, Libyans, Iberians, Gauls, etc) being organised into units in their own way. There is some evidence to suggest that the Gauls during the campaign did start to copy the organisation of the Iberians (into smaller well-organised and well-drilled sub-units) as they were alternated in the battle line during the battle at Cannae. Still, the Gauls and Iberians each had their own units.

So all the men in a unit were from the same region. The lower unit commanders had the same background as the men in their respective units. Only the higher commanders of the army were all Carthaginian. Between the lower and the higher commanders a common language must have existed (who learned whose language we don't know).

It is conceivable that there will have been some form of communication between ordinary men of different backgrounds; communicating with gestures is always possible and learning some basic words in another language is not too hard. No doubt this will have happened. We don't have a record of it though, and we certainly don't have a record of a lingua franca developing.

And remember it is also entirely possible for someone in the army to just stick to his own group and never become involved with men from the other regions. After all, everything from camping to marching to fighting happened in the context of the unit, which was just men with the same background.