In order to gain Super Speed, Lila must use the lightest equipment possible. Any extra armor would decrease her speed significantly.
In a World where Armor Is Useless, the first good hit that lands determines victory and defeat. Fighters ignore offensive or defensive strength in favor of being able to land that hit before the enemy or avoid it.
Lila is the Token Mini-Moe of the group. Her little body can't withstand a powerful attack, no matter how hard she trains. And since the group want her to stay out of combat as much as possible, her training is focused on speed.