Inquiry
Who created the Red Gate that allowed Lara to be saved?
Theories
Entity Creation
The Entity created the Red Gate. Its interest was piqued by the discussion held on its identity just prior, and sensing Lucca's regret, created a Gate for her to correct her error in history.
Lucca Creation
Presumably, the Entity was able to create Gates and change history out of tremendous feeling. Perhaps Lucca created the Red Gate by her huge regret, and exploited it with the Gate Key. Though this theory is wounded by the fact that nowhere is any evidence given that humans can create Gates naturally, and though advanced shadow magic might have that effect, even the Gurus don't display that ability, it is nonetheless canon that a human in Chrono Cross dreamt up a physical being named Turnip on the outside world. Perhaps, like Turnip, this Red Gate was made through the power of feeling, and is an extremely special case.