Aslong as you still say Lucca is so strong etc etc, then you can't deny her defence capability. If she is as you say she is, eveni f Lynx hits her with his axe thing, she should come out unharmed from the impact >.>
Also, when I meant Magical Fire doesn't burn stuff, I meant it doesn't burn stuff without the will for it to be burned. Elemental Magic burns anything since it's the element of that. Lightning, Fire, Water and Shadow are the vital parts that hold the universe. If it's magical, it's channeled in to burn the thing. Did we ever see the ground be destroyed around Crono when he used Luminaire, or the ground to be squashed thanks to Frog's Frog Squash? Did the whole Black Omen get sucked into the black hole of Magus' if you used it there? Did Lucca's fire ever start a fire which she didn't want? NO! So even if the fire is there, it should only make her own spell that much greater to finish of Lynx and such. Lucca is a smart woman, and would know how to defend herself, maybe even throwing a chair or such.
And you don't think its weird that Lucca would be by herself in that room, and Kid comes in to later view the fight. If Lucca was really truely worried, she'd have tried to escape. Desperate times call for desperate measures, so she would have used her magic to her advantage. She did not, and whatever happened, Lynx was able to beat her. And even after that, the fact that Lynx later killed Lucca (probably in Chronopolis) would raise questions as to why she did not use her magic once inside there, since it was safer to use a fire spell and such.