"I know what you're thinking: 'Did she fire six shots or only five?' Well in all the excitement I kinda forgot myself. So there's one thing you gotta ask yourself: Do you feel lucky? Well, do you? Punk?"
I'm not much for punny names...there's not much you can do with a name like Lyra but I do have somewhat of a name with meaning: Heartstrings, just Heartstrings. Why? Irony. The term Heartstrings is used to convey deep feelings, ie. "tugging at the heartstrings". Since this Lyra has a gun cocked at Tavi's head with no concern at all, it feels ironic to be named Lyra Heartstrings and be cold and nonaltruistic and possibly violent.
Just my 0.02.
And if you need her to be full Italian: "Lira Corde del Cuore" (Yeah, it just her regular name in Italian, sue me...)
And if she does hits (assassinations), her other weapon of choice can be a garrote (for silent strangulation) using a lyre string.
I have no punny name so I'll have to make do with a meaningful one.