Long term it probably doesn't make too much difference; England is England, and most of the geopolitical situation is outside of their control.
Medium term, it may depend on when it happens; a Lancastrian victory at 1st St Albans that squashes the rebellion basically before it starts looks very different than a Lancastrian victory at Mortimer's Cross or Towton, which in turn looks very different than a victory during the Barnett campaign (which would see Warwick on the Lancastrian side, and possibly, depending on the POD, Clarence as well).
Whoever is in charge would face several dilemmas:
- Dealing with the rebel lords; who these were and what resources are available to deal with them depends on when the victory happens. Especially in a 1470 victory, you have the issue that a lot of former Lancastrians have claims on land that is now being owned by former Yorkists; trying to dispossess them risks starting another round of civil wars, but not rewarding your followers also risks undermining your support base and ruining things that way. Not to mention that if Warwick and Clarence are alive and allied with the Lancastrians, they have their own sets of issues, which may or may not align, and plenty of grudges with other Lancastrians as well.
- Any surviving Yorkist exiles. OTL demonstrated repeatedly that other nations were easily tempted to use English claimants to disrupt England whenever it suited their interests; depending on when the war "ends," both sides will likely have made several foreign-sponsored comeback attempts already, so will be particularly aware of the danger. Even if a foreign power doesn't have any intention of intervening at the moment, a royal exile is a useful bargaining chip.
- France, Burgundy and the HRE. The old English claim on France was a significant political issue well into the Tudor period OTL, with Henry VIII in particular being active in asserting it as part of his wars with France. OTL Edward IV spent a good chunk of his reign planning expeditions against the French, but generally ended up getting left hanging by his various allies. What Henry VI and his successors will do is less clear, but English interests in Calais, Brittany and the Low Countries mean that they can't remain neutral. OTL Henry VII (one of the least militaristic English monarchs ever) more or less owed his throne to France, but it didn't stop him from going to war with them over Brittany a decade later.
- Scotland. The Scots are less powerful and thus less threatening, but still can't be completely ignored. The exact situation in Scotland depends on the date of the Lancastrian victory; James II ended up dying fighting the English in 1460 while his son was a child, so if the war is over earlier that doesn't happen. Likewise, Margaret of Anjou had given them Berwick-upon-Tweed in 1461 in exchange for Scottish help during the WotR; if she doesn't need to do that ITTL, she obviously won't. So depending on the exact date, the English may want to meddle in the always messy Scottish civil wars and politics, and if they have already ceded Berwick, they'll certainly want to take it back.