I DON'T KNOW WHAT IS GOING ON ANYMORE 😭😭😭
It's actually incredibly simple to follow.
A magic ring that grants wishes created a doppelganger, Lynn, of Kriemhild, the one who wished to have adventures with her husband and get along better with women, using itself as the core. Lynn's sexual fixation on Brunhild stems from the desire of getting along better with women, including her specifically, paired with Brunhild being the ring's former master. A ring does exist only to be penetrated after all.

Anyway, this whole tournament, including Lynn's existence and participation, has been a gamble by her siscon brother at creating a timeline that has so massively lost the plot, that being the original legends that this is all based on and repeatedly discussed in detail in most chapters' translation notes, that it doesn't have to end in Kriemhild's death.
This particular fight is very specifically symbolic of the core point of the plot as a whole. Brunhild's weapon is a force of inevitable fixed details, while Lynn's is one of wild deviation.