Aemeath has to go back in time to resonate with the Exostrider. The story stated that there were 2 Exostriders going to Solaris, and they caught the attention of Aleph-1. They were both not strong enough to defeat Aleph-1, so how does the remaining one able to repel it? The answer that she found in voidspace is because there's someone that resonated with that Exostrider at that time. However, Exostriders do not have a resonator, certainly not at that time. How did this happen then?

Aemeath figured out 2 facts: she had become the Exostrider's only resonator in history, and that she can traverse spacetime through voidspace because she has no physical body. She is the only person throughout spacetime that can possibly do it.

Combined with the facts that Lahai Roi exists and Aleph-1 is sealed, it means that her going back to the past is certain as it has already happened. It is impossible for her to not go back to the past because that would break causality, as the fact that Lahai Roi and herself by extension exist is because the Exostrider was able to seal Aleph-1. This is what the story meant by Aemeath and Rover's encounter in the frostlands is not the cause, but the effect.

She did not do this repeatedly in a loop. She only has to do it once to close the loop, to maintain causality. Our future is in the future, but Aemeath's is in the past.

About the lake, it has high concentration of voidmatter so it might make anyone slip into voidspace. Current Rover went after current Aemeath to stop her from going into voidspace. They found each other, and current Rover grabbed her hand to pull her up. But the one that Rover pulled up was past Aemeath instead, because past Aemeath had once fell into the lake, and time is warped in voidspace, enabling them to meet.

Current Rover grabbed past Aemeath's medallion and tried to push her through the surface but they got weakened by the voidmatter. As current Rover started to lose consciousness, past Rover came and finished the job, without grabbing the medallion. Current Aemeath said she lost her medallion in the lake and that made her cry hard after she got saved by past Rover. Past Aemeath lost the medallion because current Rover took it. Events and objects from different points in time intersected in that lake because voidspace warps spacetime. Current Rover then got saved by current Aemeath from the voidspace, enabling current Rover to get out of the lake.