I was using my Lamy Al-Star (an aluminum made Safari) with a converter. Cleaned it out in order to lend it to a friend and decided to ink another Lamy (in the picture) but, voilą, the Lamy converter in the picture (the one with the red knob) doesn't fit the Lamy pen. Fortunately, the other Lamy converter (the one identical to the Montblanc and Waterman, if my memory serves me well) fits perfectly.
According to Lamy the Z-24 converter fits the Safari, Al-Star, Vista, and Joy pens and has two lugs on the sides that mate with slots in those pens' sections; the Z-25 converter fits Accent and Persona Model 23 pens; and the Z-26 converter fits Logo, ST, Linea, CP1, ALU, Lady, and remaining Persona pens. Your pen looks like a CP1 as near as I can tell.