I really have no idea or experience if this is going to work, but if you are using samples (with the AudioFileProcessor) or presets, the tab "MIDI" has different channels. So maybe the different keys are the different channels? You would have to make one key activate one sample.
Another solution is to make or download a sf2 file. I have discovered that the different keys of some of the sf2 instruments, is actually different samples. Mostly these are different drums. So if you could learn yourself (quite easy I think) to smash together the wanted samples in a sf2 instrument, the different keys would have different samples.
I think LMMS have this functionality, it is just I who don't have the knowledge.
PS: I think the first method is not going to work for you. When you press a key on you piano, the sample will play as long as you hold the key, but stop playing when you release it.