Worth noting that the Lucifer shields were described as 'sheath' shielding IIRC, which would appear to be different to the GTVA shield types (and indeed the Shivan fighters').
Also worth nothing that fighter shielding was based on recovered Shivan technology (or scanned at least; I forget the exact details) - the Lucifer was the only large ship to be shielded, it was the only large ship to have 'beam' (like; i.e. in vprime ani) weapons, and it was also totally destroyed (and had a habit of destroying any GTVA ship that got too close).
The Lucifer is in many ways a bit of an anomaly in the Fs universe; not even the Shivans have shielded capships, not to mention that the Lucifer was originally intended to have a blood-red warp-in (from the cut Tombaugh station cutscene script). If capship shielding could only be reverse-engineered from the Lucifer, then it's quite possible there's just not the basic information to do so - I don't think there's any reason why the physics (or whatever) for shielding a large object couldn't be completely different in terms of shielding a small object such as a fighter.
The Lucifers shields quite possibly only existed to make it literally invulnerable and thus setup the grandstand finish to FS1; if you look at the roughly comparable situation with the Sathanas in FS2, the player had pretty much no role in making the 'deathblow' to it (of course, this would be offset by the simple fact that FS2 wasn't in the end about stopping the Sath).
IMO the reasons Arcadias don't have beam cannons is a) because they're too old to be retrofitted with the technology and b) they make good 'defense' mission centrepieces, and adding more beams, etc, as defense would weaken that.