Why did L sacrificed a criminal in the episode where he wanted to test Kira (World broadcoast) knowing that L is against the killing even if they are criminals

He wanted to test his theory also the man was going to be executed so he be dead even if it did not work.

because the criminal would've gone too his execution anyway

Because it was the day of his execution first off and second, he didn't actually think that Lind L. Tailor would die just like that. He didn't believe in Kira's powers at first until he saw it with his own eyes.

L is willing to bend the rules, it's just his nature. He did this because it was for the greater good, what's one life to stop 124,925 people from dying? (That's how many people Light killed btw)