The Lady of Pain enforces the Law against Dieties & Archfiends (in cannon at least, by barring the portals or Flaying the dieties in question.)
I am interested as to how this siege was accomplished, as the Lady can simply cut off portals (all of them). And since she neither cares for her subjects nor requires anything that might resemble sustance. Add this to the fact that many of the more powerful casters are able to simply conjure food, water, and remove their need for air. This might lead to food riots and death among the Hive and Lower quarters but it would have little effect on the Lady who bars the gates to the cage.
Beyond this, how would you hold Sigil? Pit fiends on up are barred from the city of doors, by the same rules that you said would force out the Lady.
By extrapilation, the immutablity of Sigil's portals would also be kept as a property of the city. So now you have a staging point (admittedly a farely good ones) but the problem becomes, many of those portals are 2 way. And Sigil portals cannot be sealed or barred on either end.
Now many of your troops are stuck in a centeral place where the enemy (Small groups of celestials, Adventurers, Neutrals, etc.) can hit them from any and every direction. That would actually be kind of cool to watch, as level 15+ adventures, or non-barred planars strike like the Vietcong against the Baatezu and Tanarri. The cost in "lives" would be staggering just to maintain nominal control of the city. It would likely devolve into a Seravo like warzone, with no group having the resources city complete.
Other questions. Who is leading this army of Evil? Who has enough prescenese that both groups would follow them as a cohessive enough force? What is their command structure? How are they supporting their war efforts? Communication? Supply Lines?, etc.
Can they even dent Ysgard (with automatically True Resing Petitioner Armies that are fully trained)? Can they move in Elysium (The plane activalely manipulates its struture to prevent them from committing evil, how fast you travel = how good you are)? Do they even dare Mount Celestia (7th layer being what it is)
How are the Elemental Lords reacting to the horde? The Rilamani? Slaadi? Modrons aka Primus?