Can anyone tell me why Vito would send Luca to Tattaglia's night club under the ruse of being a traitor in The Godfather? The relationship between Vito and Luca must have been well known in the mob community and Vito would have known that. Are you going to tell me that Vito didn't consider the fact that Tattaglia wouldn't buy that his story of being unhappy with the family? If Vito is as sharp as they would have us believe, why then would he send his most trusted soldier to his death? I believe this is a flaw in the plot.
There was no one in the Corleone crime family more trustworthy and loyal to the Godfather than Luca. Luca almost never appeared in public with the Godfather, or really any of the rest of the family members. This was because Luca wanted to ensure Vito's reputation was not ruined from association with him (Luca.) Because of this, it would be believable that the other Bosses and their Capos would not be completely knowledgeable of the extent of Luca's loyalty, or why it was so.
Who else could Vito send to entreat with Sollozzo? He might have been able to trust his own family, but really at the time this all happened, he was still trying to keep Michael away from the family business, Sonny was too hot headed (and spoke out of turn) and Fredo was ... well weak.
No, the only person Vito could completely and implicitly trust was Luca Brasi.
Remember also, that the things we know, as the voyeurs into the mob as watchers of the movies/readers of the novels, are not known by the characters themselves. Sollozzo and Tattaglia don't necessarily know (for sure, with absoluteness) the extent of Luca's loyalty. Luca went to one of the Tattaglia nightclubs and complained about lack of money. This would have been a sure signal about perhaps turning Luca.
Compare this to the (real life) Iceman, Richard Kuklinski. While he never had the loyalty to his boss that Luca was supposed to have to the Godfather, he was a ruthless mob enforcer. While the movie (Iceman) is based on the true story of Kuklinski, I am sure much of it is (unsubstantiated) drama. However, we do see in that story that when the boss, DeMeo, is forced to curtail his family's illegal activities, he benches Kuklinski, which causes K a great deal of financial distress, directly leading to his (K's) eventual downfall and arrest. So, you could see that, from the outside, Luca, like Kuklinski, might have a weakness (debt).
At the time Vito sent Luca to Sollozzo, he (Vito) was 'under fire' from Sollozzo and some of the rest of the bosses for his refusal to embrace drugs. Vito Corleone's power was in his ties into corrupt politicians and the police. Sollozzo (and his Capo Tattaglia) needed Vito's politico connections in order to more successfully promote their drug trade. Remember that the whole mess contained in Godfather (1) started with the meeting between Vito and Sonny and the other bosses (wasn't it Sollozzo?) where they needed his help. Sonny spoke out of turn during it. The whole feud would have caused a drop in the Corleone family businesses and perhaps as a result, Luca might be driven to find outside income.
(All of the above is based on the novels, the movies and the wikis).
Though in the movie it seemed that Luca went straight to Tattaglia's, but its not the fact. As per the book he stayed on Tattaglia's hotel and the word was on the air that the relationship between Corleone family and Luca isn't so well. Then the Tattaglia's called Luca to meet them. And Godfather sent Luca because he was the strongest and fearing. Anybody would consider twice to kill him and Luca isn't dumb either. He sent the strongest to deal with the enemy. Its not bad decision to make.
I have always felt that Vito was trying to get rid of Luca. If you recall, Vito acts in disgust when told that Luca was there to congratualte him on Connie's wedding day. As Luca stumbles through a carefully rehearsed congratulation, it becomes apparent that he's a little "slow". Like Fredo, but Vito would never do anything to Fredo. I always felt like it was a double move; he got rid of Luca and planted a seed in Tattaglia's mind that Tattaglia can't quickly recruit because he might end up recruiting another Corleone member accidentally.
I think Vito didn't want to send his immediate family. Combative Sony, precious Micheak and incompetent Fredo to the invaluable Tom Hagan. I think he wanted to test how serious Solozzo was and sent someone he knew would march into certain death without question. Luca was more loyal than dumb and Vito knew if anyone can walk away from the meeting going sour, it would be Luca. He rolled the dice but before he could deal with the seriousness of it, there was a hit on him Iit's chess not checkers.(damn Fredo, damn Pauly)