*Side story*
This is a side story of how Lex discovered and unlocked his Haoshoku haki
One day when he was 6,he was walking in the town with his guards, Lex thought he could only see the real town without his guards, so slipped through the guards and entered a dark alley,here he saw two drunks fighting each other and kicking a little kitten on the ground,Lex recognised this kitty as the one which came around when he trained so he decided to intervene and shouted at the men,"You piss-ants stop bothering the kitty and go away".
The drunk men got angry and sized up Lex, they saw that he was wearing expensive and designed clothes so they men looked at each other and nodded simultaneously and then pulled out a pistol and aimed at the Kitty,"Oye brat,if you don't want your precious kitty to die then pay up", the man was not kidding.
Lex was highly disturbed,"Damn the other guy is blocking the way, I can't reach him before he pulls the trigger and I only have about 1000 belly with me"
Just like that Lex threw the purse which had 1000 belly at them,"Here is your money that's all I have on me so now let that Kitty go!"
The men opened the purse and found 1000 belly which ticked them,"Don't screw with us kid,we know you are noblity so quite screwing around and give us more".
Lex was trying to calm them down,"It's all I have I swear,you can come with me and I'll get you more but for now let go of the kitty".
"You really take us for a fool kid? Fine have it your way we can't kill you but killing this dumb kitten is no problem", the drunk started pulling the trigger when Lex started screaming,"NO WAY AS*HOLE,LEAVE THE KITTY ALONE"
*Whoosh* waves surrounded the area started and Lex's will pushed out towards the two men knocked them unconscious.
Lex stood there dazed as the two men fell and looked around as nearby people also fell, that's when he realised that he had Haoshoku Haki.
Yes,yes this is similar to Luffy, but it's usually in stressful situations that they unlock Haoshoku Haki so this suits the narrative