Friends and family have raised more than $8000 for the Gibsons, with one relative describing the tragedy as "the worst possible scenario imaginable".
The relative said: "Without any explanation, a three-year-old beautiful, happy baby girl was taken from a kind, loving family.
"Lily passed away with absolutely no warning whatsoever and there was no way of preparing for the loss. To lose a child under any circumstances is horrific, to lose a child while on a family holiday when it should be a time of joy and love is hard to even fathom.'
The coroner's court heard that Lily was taken to a walk-in centre with "yellowing" of the skin - a symptom of jaundice.
The parents were given painkillers for her and sent away. Assistant coroner Professor Robert Forrest said there had been a reported anecdotal increase in illnesses at the hotel around the time of the Gibsons' holiday.
He said: "The evidence of poor food safety at the hotel and the possibility that Lily died as a consequence of a food-related illness provides justification for additional inquiries of Thomas Cook."
A Thomas Cook spokesman said: "We have provided the coroner with all the information we have been able to gather from the hotel and healthcare facilities."