These sorts of conflicts in tuning arise, as Urs pointed out, from using one note to designate two different harmonic contexts. The whole field of temperament is largely an effort to reconcile them, with varying solutions in various time periods, depending on what kind of sound was preferred (for example, in some meantone temperaments you hear much purer thirds, at the expense of fifths being too low. In others, you have exactly the opposite). In just intonation, I would describe the two kinds of D -- a fifth over G and a major third over Bb -- in the key of F as 27/16 and 5/3, respectively (and they have, as you note, a difference between them of about 20 cents).
There's reasonable benefit to giving cents values, beyond educational: one of the conventions in just intonation -- one which a colleague of mine really wants to see -- is to approximate the accidentals to 12th-tones (so, 12 steps to the whole tone), and then give a markup above indicating the nearest semitone with cents deviation. In the case of our 5/4 third, that would show "D -13.7" above, but the accidental would be a D 2/12th flattened. Other instruments, which maybe can't use 12th-tones, might use other kinds of accidentals, which behave according to different rules (for example, there are common fingering charts for flute and oboe that give 8th-tones, but clarinet just has quartertones). Being able to specify an exact harmonic ratio, and then have Lily output different accidentals, each behaving according to different rules as needed, would be a big advantage over other software (and would open it up to systems like mine, which behave according to totally different rules which can nevertheless be extracted from the information given).
Cheers,
A