There are two interlinked problems to a lingua franca that works for multiple sentient species. One is, as you have said, that the lingua franca would have to work for species whose means of speech varied between "Whistling, grunting, radio-waves, exchanging proteins, exchanging electronic data etc etc..." The other problem is deeper and more difficult.
Problem number one could be dealt with by having the common part of the lingua franca be at the level of conceptual structures; the part of grammar dealing with basic classification of nouns and verbs and adjectives - or something even more universal than these divisions. Then on top of that there would be the actual means of speech, which might vary between species but could probably be translated by computers or people given that the grammar was already the same.
There is a real life example of this sort of thing now. As you probably know, the various sign languages used by the deaf, such as British Sign Language and American Sign Language, are languages with a grammar very different from the spoken language (English) in the same territories. For instance sign languages, being received visually, often use the fact that information can be relayed from the face and the position of the hands simultaneously. However when people go deaf later in life they often find it hard to pick up a whole new language such as BSL or ASL, so they use Signed English, when each word is signed in the order that it would be spoken in English. It is "clunky" compared to the true sign language because the necessarily sequential nature of a spoken language adapts badly to the more "parallel" nature of a gestural language. But it is easy to learn for a native English speaker and works as a sort of lingua franca.
Problem number two is more profound - what if the thought of aliens is so, well, alien that we simply cannot find common concepts?
We could only establish whether an alien species shared enough common concepts to build a lingua franca between them and us by trial and error. We might be spared the bother if other established spacefaring species interacting with each other had already done most of the work for us. All we would need to do was add the specific English / Mandarin / Hindi or other local surface layer to the off-the-shelf translation machine that comes with the Galactic Federation welcome pack.