Is this what the world needs right now: another conspiracy drama about how we were lied to over the Kennedys and Marilyn? Torben Betts' new play does at least have a fresh historical protagonist: Dorothy Kilgallen, the Pulitzer-nominated journalist who interviewed Jack Ruby in prison after he gunned down JFK's assassin Lee Harvey Oswald in public and was herself found dead, like Marilyn, from an overdose of booze and barbituates.

It also has the reliably luminous Janie Dee as Kilgallen, and heavyweight director Trevor Nunn at the helm. Kilgallen's a fascinating figure to disinter, and Nunn's production has gravitas, and a couple of outstanding performances, but ultimately I wasn't persuaded: by the speculations on whodunnit, or by the drama. Betts' play is subtitled On the Unexplained Deaths of Several American Icons - which is a lot of speculation to wrap up in a two hour stage play. There are three scenes, which unfold in instalments. First, Kilgallen's New York apartment where she types, swigs vodka and confides her theories to a fictional Black babysitter she's only just met; then Lee Newby's fantasic modular set swivels open to reveal an underworld bar where Lee Harvey Oswald (a nicely twitchy Joseph Potter) is being groomed by a crime boss; finally Marilyn's last night on earth, imagined as a deadly confrontation with Bobby Kennedy.

Betts' play is more of a whydunnit than a whodunnit: we know from the get go that Bobby, Marilyn, Dorothy, and Lee will die, and it's fairly obvious from which direction these shots are coming. There are some good lines about journalism, theatre and politics, and all three actresses really shine. It's a thankless task to play Norma Jeane – what actress wants to be compared to Marilyn Monroe? But Natalie Dunne finds an appealing sensual and emotional rhythm in her arguments with Bobby about the wife and kids, and made me care about her fate. And Gloria Obianyo is outstanding as the fictional babysitter Flo, even if it’s a bit part that's made to carry far too much context (Vietnam; the ’60s civil rights movements; racism in America). I found it a bit implausible that a babysitter would spend so much of the evening listening to Kilgallen's theories and so little looking after her son.

Dee is always a dream to watch, but the play suffers from too much exposition and, because we know what's coming, not enough peril. It feels scattered and unsettled. This material has been sifted endlessly by generations of journalists, conspiracy nuts and redditors; it's both overfamiliar and far-fetched, which makes it harder to care about the characters here. Were the American people lied to, about Kennedy, about Lee Harvey Oswald? Probably. But it now feels quaint to imagine that a movie star might have been murdered because she wrote some gossip in her diary about a plan to assassinate Castro. The speculations are intriguing and Nunn has put together a well-crafted production. But in an era where political lying has gone beastmode, to the algorithmic next level, this just didn't feel to me like an urgent story to re-tell.