Why was it necessary for Lady Olena, Peter Baelesh and Ser Dontos to conspire together to give Sansa a necklace containing poison?
Given that Lady Olena was essentially just pouring poison in to Joffrey's drink - couldn't she have just had the poison kept in her handbag or something?
Why to the contrived effort to involve a necklace and other person?
I'm interested in answers concerning both the TV show and the books.
It wasn't necessary. But... If you can kill three birds with one stone, wouldn't you try to?
This, I believe, is the primary reason. Littlefinger has never got over his first love for Lady Catelyn. Aside from that, as the eldest legitimate Stark alive, she is a valuable pawn. The poisoning of Joffrey is followed by Littlefinger "rescuing" Sansa, bringing her to his home, and then to the Vale. And at the Vale, they have a short kiss. Events diverge between the book and the series here.
In the books, Sansa is set up to marry Harry the Heir, the person most likely to inherit the Vale if Robert Arryn were to die.
In the show, Sansa is married to Ramsay Bolton, returning to Winterfell. This is later on used to provoke Cersei into believing that the Boltons have betrayed them.
Tyrion's lack of respect for Joffrey is well known, as are the numerous abuses that Sansa has suffered at Joffrey's hands. By framing these two, the actual conspirators gave the investigators (if there were any) a very culpable-looking pair of conspirators, thoroughly deflecting attention away from themselves. Why would anyone look further for the perpetrators? Yes, Sansa wasn't caught. If she were, and if someone suggested checking the necklace, it would have been damning evidence. As it is, Sansa's absence is considered damning by itself.
Admittedly, I don't have any evidence for this last part. But if I were planning an assassination, and I have someone on hand that everybody would believe to hate my target, I'd be looking for ways to frame them.
Lastly, also speculation on my part, but weak: Tyrion was a good ruler, and had become a strength for House Lannister. Neither Littlefinger nor Lady Olenna have any particular interest in Lannisters remaining strong. Humiliating the Lannisters and eliminating one of the best of their House would have been sufficient motive by itself.
