It's close from being ASB, the whole conflict turning to a war of attrition that fiscal policies of England couldn't withstand on the long run. It asked for a full-fledged civil war to have Lancaster managing to hold 1/4 of the kingdom, without any real means to advance than pressuring as much they could an already scortched region.
Simply said, in matter of ressources, politics, legitimacy and logic, England couldn't have "won" HYW (as in having Plantagenet/Lancaster dynasty taking over).
Now, assuming (
and I must stress that we're talking about something particularly implausible) it's done. What do we have?
A dual kingdom : with two different structures, fiscally, administrativly, military; on which french ones are going to prevail.
Giving that a king of France does hold more important and prestigious power (there's a reason why Plantagenets arms put France's arms on the first position, and Lancasters
twice), without any reasonable doubt, the core of Plantagenet/Lancaster is going to be in Northern France and in Paris.
Why? Because we're talking about what was not only the main city in the kingdom but in the whole of western Europe; and on which the bulk of the French administration was already present.
And let's be clear : in order to fund this dual kingdom, their rulers aren't going to recieve much of the English Parliment. Going to Rouen or Calais would makes approximatly as much sense than having the British capital being set in Newcastle upon Tyne to please everyone.
What would be the situation in France? In all likeness Burgundy holds at least half of the kingdom under its hands : not only trough fiefdoms but trough the
Bourguignon faction within all the kingdom (and that would definitely be at the core of anti-Lancaster activity, Valois-Bourgogne appearing now as the most likely candidate for a French restauration).
And that with an England more and more frightened by the increasingly French influence. It would be like Vietnam trying to swallow up China : it's not going to be the smaller, less wealthy and far less inhabited country that's going to integrate the other.
And giving the rise of national feeling, the fact that French kings had already a more important power over Parliments (and the fear of a political unification at the expense of English Parliaments' freedoms). That's simply *not* going to end well.
To resume : A Lancaster king stuck between an uncomfortable ally at his right, and a growingly dissatisfied England at its left.
If it doesn't ends with a general collapse...