How funny; I was just daydreaming about a crime boss-like champ a few days ago. It's only a barebones idea, very fuzzy, but I'd be glad to share a few ideas (if only to get them out of my system).
The crime boss's background is someone who's made a criminal enterprise in Zaun off stealing and bootlegging technology from various inventor groups. He and his thugs reverse engineer shoddy knockoff gadgets to sell in other cities, too. The only things keeping away the scores of enemies that want him dead are his ruthless ambition, ceaseless alertness, and cunning sharper than his stilettos. But even that might not be enough to save him this time. They perhaps went too far in stealing from that batch of scientists developing exotic weapons. Their response was more painful than anticipated and decimated a chunk of his crew. Analyzing what went wrong, he vowed never again to make the same mistakes. Determined to rebuild, even expand his operations, he joined the League to make his name known and learn which big dogs he'll have to one day put down.
Regarding his abilities, I couldn't get anything concrete down, but I got a few possible concepts. I imagined a kit that reflected a paranoid, commanding personality as well as his technology thieving. His abilities would revolve around using gadgets to control the battlefield while other passives would benefit himself or his team (in his eyes, why not let them do the dirty work?). As such, his role may be support/marksman. I'll list some ideas below
He throws knives for autoattacks.
Passive: Paranoia. (Idea 1) Gives him a burst of movement and attack speed when an enemy suddenly enters his vision. (Idea 2) Gives him a burst of movement after holding still for a few seconds
Passive: Big Haul. Grants him and nearby allies more gold from kills.
Gravity Node: Boss tosses a gravity node (about the size of Grave's smoke bomb or so) onto the field. These nodes are shoddy and will fall apart after a short while. Enemies that walk into the range around the node are either pulled in or repelled based on what ability is used, and take damage from those actions. Another viable ability is to have electricity arc between the nodes.
Charge Disc: Boss throws a frisbee with a refreshing amount of voltage. Allies it passes through get an attack speed and damage boost. Enemies it hits take damage and are slowed for a short duration. The disc explodes after flying to its max distance.
1, 2, 3!: The next three autoattacks have increased damage and vastly increased attack speed. This may be paired with a passive so the ability slot isn't so empty.
Ult: Open Game. Reveals all enemies on the map for a duration and grants his team bonus gold upon killing enemies.
Ult: Absolute Rubbish. Detonate all gadgets on the field, creating powerful explosions.
The node was the core idea I had, that the Boss lays out nodes to pinball foes or pin them down for allies to kill. How the nodes switch between pulling and repelling, I'm not sure. They also make it hard for foes to get close to him. Combined with his speed buffs and debuffs, the Boss can jump in and out of his "playground" whenever he pleases (if he doesn't mind letting others play in it). He may be squishy, but that doesn't mean anything if they can't catch him.
That's pretty much all I got. I got nothing on how he would relate to other characters in the league, but I agree with Xedrekk that he ought not be all too connected with Cait or Vi. Exploring a new angle would be less constrictive and world building. Hope this helps!