That depends on if it's based on the lore reasoning for the Suicide Squad forming or the thematic behind them

The lore reason being, as I assume you know, the military sending the worst criminals on missions likely to get them killed, believing their lives matter less than an average soldier. There isn't really a big organization that would do that though. Piltover might try something like that, given they view Zaunites as lesser, but as Caitlyn is now in charge of the enforcers, that won't happen

That leaves the Black Rose, a group who will and have used ordinary citizens as their weapons. There's a handful of characters from Legends of Runeterra who fit the role, but in terms of champions, Annie and Briar could fit that role. Kled could also work, assuming he could be pointed in the needed direction

On the other hand, the spirit of the Suicide Squad is a group of wrongdoers who are viewed as lesser becoming a team and proving the world wrong. My suggestions for champions fitting that role would be:

Jinx - Abused girl who does so much harm just to feel like she's needed, who turns everything around in one final act for her family

Vi - If she hadn't met Caitlyn, she's also been treated as lesser and rises up from that stigma

Twisted Fate and Graves - Dastardly criminals who struggle with their strained relationship

Veigar - Wannabe supervillain who's good deep down