In my opinion, [Lesion] is one of the only melees that can run Viral and Slash on the actual melee and perform about as well as a basic light attack pure Slash build.

[Gladiator Vice]
[Gladiator Vice] does two things:
1. Attack Speed
2. It allows this weapon to [Reach] 100% CC

The great thing about [Lesion] is that it gains 15% Attack Speed upon proccing any status effect. This allows us to freely mod [Gladiator Vice] for extra crits without needing to double mod Attack Speed, which we literally don't have room for. Unfortunately, it does still feel slow at times, so Arcane Strike is recommended.

Rivens
In theory, Rivens can do what [Gladiator Vice] does, but better right? Well on a 3+1 god roll (CC+AS+CD+Neg), at most you only get ~11% more Attack Speed and ~5% more CC. You do get an extra ~24% CD buff, but for that large of an investment it's not really worth it. What about a 2+1(CC+AS+Neg)? This time you get at most, ~19% more AS and ~11% more CC. Again, not really worth it in my opinion. So yeah, Rivens, not really worth it for this specific build.

[Vicious Frost]
This should be common knowledge by now, but VF is purposefully left at r1 to maintain slash weighting.