Well, knowing Katrina, she would want the units to ba able to make it back, I would not be suprised if her task force came in through the Alberio Prefecture, after skirting the FRR, minimising the chance of detection.
Such a knockout blow would need to contain troops from all sectors of the realm, firstly to make it an AFFC action, not an LCAF or AFFS one.
Looking at spare units in the Lyran Commonwealth in Historical:3039, this what I would send in, leaving already assigned units alone, so as not to generate suspicion from the DCMS:
UNIT (Experience/Reliability/Equipment Rating/Post in 3038)
20th Avalon Hussars RCT (Vet/Fan/A/Freedom)
6th Crucis Lancers RCT (Vet/Rel/A/Loburg)
4th Deneb Light Cavalry RCT (Reg/Rel/A/Alcor)
4th Donegal Guards RCT (Vet/Rel/B/Chateau)
14th Donegal Guards RCT (Reg/Rel/A/CMO 26)
6th Lyran Guards RCT (Elite/Rel/A/Althastan)
2nd Royal Guards RCT (Reg/Fan/A/Tharkad)
The Bad Dream (Vet/Rel/A/Newtown Square)
3rd/12th Star Guards (Vet/Rel/A/Icar)
Approx Force: 9 Mech Regiments, 15 Aerospace Wings, 21 Armoured Regiments, 35 Infantry Regiments
Facing them on Luthien would be:
UNIT (Experience/Reliability/Equipment Rating/Post in 3038)
1st Sword of Light (Vet/Fan/A/Luthien)
7th Sword of Light (Vet/Fan/A/Luthien)
Otomo (Elite/Fan/A/Luthien)
Dragons Claws (Elite/Fan/A/Luthiem) - They may have been available at this time.
These additional units are based on what is presented in Luthien.
3rd Aerospace Wing (Vet)
7th Aerospace Wing (vet)
Black Dragons Aerospace Wing (Vet)
6th DEST (Elite)
These units are likely armour and infantry
12th Luthien Defence Regiment (Reg)
54th Luthien Defence Regiment (Grn)
96th Luthien Defence Regiment (Vet)
122nd Luthien Defence Regiment (Reg)
143rd Luthien Defence Regiment (Reg)
178th Luthien Defence Regiment (Reg)
191st Luthien Defence Regiment (Reg)
201st Luthien Defence Regiment (Reg)
7th Imperial City Militia (Reg)
1st Amori Militia (Reg) - Combined arms battalion
Luthien Armour Works Security Company (Reg)
Anti-Mech Infantry Regiments
1st Omega Regiment (Vet)
2nd Omega Regiment (Reg)
Approx Force: 5 Mech Regiments, 7 Aerospace Wings, 5 Armoured Regiments, 20+ Infantry Regiments
If I was the AFFC, I'd also toss in a couple of Assault DropShip wings and an Independent Aerowing or three.
It would be a savage battle and the AFFC would want to leave after a month of dismanteling DCMS units and infrastructure as by that time Alshain and Pesht units would start to arrive. I don't think the task force could hold the world, but they could wreck it and cop 50% casualities doing it.