If your opponent has no SIGNI that can be banished by Fires of Atonement in the first place (e.g. not having any SIGNI on your opponent's field before using this card), your LRIG still gains double crush.
If Fires of Atonement would banish a SIGNI, then that SIGNI becomes an illegal target for Fires of Atonement (due to being put into the trash by Bloody Slash or its power is increased to 13000 or more by Fantastic), the spell is canceled and your LRIG does not gain Double Crush.
The possibility of a SIGNI being banished has been removed by the ability of Lucky Guard, but not as if the original target of Fires of Atonement was made illegal. Therefore, it is simply considered that Fires of Atonement cannot initiate the banish ability, and proceeds with the rest of its ability (granting your LRIGDouble Crush).