This is a little off topic, but someone with a better understanding of the RD plot could help me out...
In the RD reality, what is the role of the Frozen Flame?
This is random banter on my end, but if the Frozen Flame's role in RD is the same as it is in CC (certain magical/energetic properties that seem to "grant wishes", to a degree), then perhaps RD takes place in a universe in which the Chrono Trigger either doesn't exist, doesn't work, or was never given to Crono and company.
My logic in this assessment is that Lucca wants the Frozen Flame to put on a friend's grave. The only friend we know of, and if I understand correctly, RD points towards this deceased character being Crono. Knowing that Crono was killed in Lavos, and seeing that we have no other instances of Crono dying, it just seems logical to me that Crono was never actually revived. Thus, perhaps, Lucca's goal was to obtain the Frozen Flame and potentially revive Crono?
Just a random thought. I'm sure this connection has been made by others - it's nothing monumental.
(sigh) Speculation is a bitch.