Honestly, in any competition that doesn't involve direct combat, Lucy could be all kinds of hax. Fairly intelligent and with a wide degree of versatility, as well as her power basically allowing her to summon advisers for second opinions and tactical help, as well as copying enemy powers (and knowledge) and weakening any humans that are around.
Heck, during the Hidden match, she could have used Virgo to hide under ground, have Gemini pretend to be her or another of the competitors if it gets the opportunity (as well as summoning as well), and had Caprico weaken any humans that came near her which might count as an attack and get her points while it shouldn't affect the illusionary clones.
Or heck, have Gemini touch Makarov before the fight (because there's pretty much no situation where having Makarov on your side if you wish would be a downside) and use Fairy Law. Lucy +Everyone but Juvia, no one but her and Juvia able to continue the match.