Getting a believable, fully synthetic singing voice is pretty much the apex of voice synthesis tech.
If you're willing to settle for (or maybe even hoping for) something less natural, you could try passing a regular text-to-speech reader through a vocoder. Not sure yet whether the whole thing could be done in LMMS, so I'll toss a +1 on this thread.
I'll suggest a simple UI for it, too: double or middle click on a note in the piano-roll to edit a text box. LMMS synthesizes the word/phrase/syllable (probably using some existing 3rd party program) and stretches it over the duration of the note, using it as a modulator for the note's carrier. Another input option might be to drag/drop words from a text box onto the piano-roll notes.