A British Gangster who is dying flies to the States, with his gang’s money, to see the old West in search of a perfect end to his once violent career.

If, as Richiev suggests, he wants to go out with an old fashioned Western shootout, the logline needs to say so.? Like:

A British Gangster dying of cancer seeks the perfect end to his violent career: a shootout at the O.K. Corral in Tombstone, Arizona.

If, as Richiev suggests, he wants to go out with an old fashioned Western shootout, the logline needs to say so.? Like:

A British Gangster dying of cancer seeks the perfect end to his violent career: a shootout at the O.K. Corral in Tombstone, Arizona.

I like this one... there's a protagonist with a goal, and the obvious threat of conflict, but, the only thing I'm iffy about... this "perfect end" in "the old West" seems a bit ambiguous.? I can see maybe he wants to reach the Alamo, or maybe the town where his childhood idol, Billy the Kid died.? You show the British Gangster while a youth, and have it tie back to that, speaking to the romanticism of violence in our culture.? I think you explain the purpose of his goal nicely in your logline, but I think it's simple enough to add a specific plan without making it too wordy since you can just replace "to see the old West".