Ok, I know this is an old thread, but anyway. I just had the conversation with Takemura at Tom's Diner. After reading all the comments here (thanks a lot guys) This is my conclusion:
Takemura knew Yorinobu from long back, he knew (everybody knew) the father and son had a bad relationship. He knew about that time Yorinobu quit to Arasaka and started his own gang. To his eyes, Yorinobu was nothing but a spoiled brat, playing rebel.
Then, Yorinobu stole the relic, and thus, committed treason. The same Subaro says so, something like "I could forgive you for everything, except treason". Even if the emperor never verbally expressed these feelings to his bodyguard, Takemura was not blind. Betraying the company is to betray the father, and from betray to murder there is only a little step. So, when Yorinobu claimed "somebody poisoned" his father, Takemura didn't buy it, but he played along.
When you are hiding inside the pillar, Takemura is thoughtfully scanning that zone, he 'feels' there is 'something' there, but he is interrupted by the emperor and forced to leave the room.
Dex tries to wash his hands out of the whole mess (or at least buy some mercy) by selling V. He is probably dealing directly with Yorinobu (as he tells V something like "I want to do business with Number 1 and you are in the way" before shooting V). Yorinobu is afraid that there is a witness he must deal with, so he orders Dex to kill V.
Now, Yorinobu has 3 loose ends he must tie:
1) V: Yorinobu has no way to know if Dex actually killed V
2) Dex: He knows too much
3) Takemura: Yorinobu never actually trusted him.
In order to deal with this in the cleanest way, Yorinobu sets up for all the loose ends to be in the same place at the same time. For this, he orders Takemura to "take Dex and go to the place where the body of my father's murderer is, and bring the body to me", and orders these corpo bots to follow Takemura and kill them all.
But Takemura has his own agenda, so when he meets Dex, they have a 'smooth talk'. From Dex, Takemura learns that V was in the suite at the time the emperor was killed; that 'something' Takemura felt when he was scanning the pillar turns out to be a 'someone'. When they go to the dumpster, to surprise of both of them V was actually alive. Seeing that Dex is no longer required, Takemura kills him (also because of honor and shit). V is Takemura's best chance to know the truth (and maybe even a witness of the emperor's murder?).
As Takemura is still pretending to be loyal to the spoiled prince, he calls him and tells him that "i've found your father's killer", but he intentionally omits the little detail that the killer is still alive. Takemura takes V and starts driving, most likely he doesn't have a plan or a clear destination yet as he just discovered that V is still alive, but before he can come up with something, the corpo bots show up and shit rains.
And, when they are at Vik's clinic, I guess Takemura took advantage of V's current mental state and interrogated him (or maybe V started talking due to the pain killers), something V doesn't clearly remember. Now Takemura knows what actually happened, and needs V as a witness.