If she had distance on Lucy (aka was out of reach of the girl's vectors) and used her flute to trap the diclonius in a genjutsu, then she has the possibility of winning. Especially if one considers the fact that Lucy is rather mentally unstable and prone to falling into a state of hallucination/amnesia; this should reinforce any illusion-based moves that Tayuya directs towards her. However, that move has been shown to be her trump card, so chances are that she would start her offensive strategy using her summoned demons.
These Lucy could deal with easily, due to the untold strength in offense and defense of her vectors when she is within range. By the time Tayuya realized her demons were dead, Lucy should already have dispatched the Sound nin, as well.
In other words, bloodlust battle/using their greatest techniques, Tayuya wins as she can trap Lucy mentally, rendering the girl's vectors harmless as they can't be used. However, any other form of fighting would result in Lucy tearing Tayuya to pieces in a matter of seconds.