PB:FttP happens after Correction Nine project was closed. Correction Nine's technology was sold to Humans and Falkonians.
Which means, that the Falkoks have Correction Nine weapons, and after the Marine travels to earth, Noir Lime could have found the Minigun C-02m, which is a weapon developed by the Correction Nine, take it, and then travel back to earth with it.
And that's how Noir Lime could have acquired the Minigun C-02m.