Except we're basing it on the fact that Kid supposedly saw it when she was 6 years old in a burning building. We even get to see the scene she remember Lynx being there, but we never see Lucca killed.

Crono only says that Lynx and Harle's mission to capture her to remove the Promethius circuit failed... he never mentions how it failed nor does Lynx/FATE or Harle.

The only evidence "she's dead" is from Kid saying so, which due to the time it happened is very unreliable evidence. In terms of evidence, eye witnesses are the most unreliable when building a case.:rolleyes2

She's alive dammit! Face it! The Great Lucca is just hiding out in the world of Xenogears until things cool down in her own dimension