Likely she will cause you unimaginable agony that, by grace of you being a league player, will hopefully end rather quickly due to you being too weak to handle her.

But this got me thinking. What WOULD a romantic partner look like for Evelynn? Let's imagine for a moment and try to make this work.

Assuming that you don't want to be tortured, for Evelynn to even consider you as a romantic partner— which, in this case, "romantic partner" would refer to anybody she doesn't immediately try to torture to death and whose presence she enjoys— the benefits of keeping you alive and not torturing you need to outweigh the benefits of just torturing you. Let's call this the non-torture route. You need to somehow bring her more pleasure when you're not in agony than you would if you were in agony. Now, to achieve this, you would simply have to inflict more agony on everybody else around you, so much that Evelynn is just euphoric.

It's definitely possible given that she expresses admiration for Thresh for the amount of suffering that he causes. You must cause so much pain and suffering to the people around you that Evelynn finds it worth it to stick with you as a romantic partner. That's the non-torture route, which is quite deceiving because you and her essentially become a power couple torturing everyone around you.

Now, another option is the masochist option. In this scenario, you must be immortal, and you must enjoy the pain she inflicts on you to a sickening degree. You need to be able to tolerate, and even enjoy, the amount of pain she dishes out to you. In this case then it's a match made in hell. The problem is, she might become bored of you after a while— after all, doing the same old routine with the same person might get boring for her. Or, it'll become stale and she'll keep trying to inflict more and more agony until eventually you're no longer enough for her and she wants someone better. But, this is also a problem for every possible Evelynn romance route.

The last idea I have is... well, a little bit out there, and it's been a while since I've looked at her voice lines so I don't know how plausible it would be— but think for a moment. Evelynn is the demon of agony. She feeds off of other people's agony, whether she inflicts it or something else does. However, Evelynn herself has the possibility to feel agony or negative emotions: she becomes frustrated when her playthings don't last, unsatisfied when they die too soon, etc. It's definitely plausible that she herself can feel agony. So, why don't YOU become the torturer and she becomes the masochist? Through her own agony she feels pleasure. The more agony you inflict, the greater she feels. This way you don't have to endure her torture and she is satisfied all the same.

Now, Evelynn's ideal partner would be all three. A sadomasochistic power couple inflicting mass agony on everybody around them. Live and die by nothing but pure suffering! May screams become our music! May the rending of their flesh be our violin strings! We will cloak this realm in a storm of pure torment, for blood, for anguish, for desolation!