Savoy seems a rather poor match for the king's eldest sister. Also, here there's no Margarethe of Austria-Burgundy to displace her, which means she'd most likely get first jump at the French king. And France is going to be wanting that match even more if Plantagenets are ruling in England and Burgundy. The only other match, besides Anne of Brittany - who I assume has either been married to Charles VIII here or not been born or died in infancy - mentioned for Charles VIII was Charlotte of Naples for a brief minute between Margarethe of Austria and Anne of Brittany. Now, Elizabeth can be married to Charles by Louis XI's death, whereas Anne is likely to still be in single digits. And her being replaced by Isabelle/Elizabeth of Burgundy makes no sense, since Isabelle would have two brothers ahead of her, plus a surviving mother as duchess-regnant, unlike Margarethe, who was heiress presumptive once Marie died in a freak accident OTL (which was why the French threw Lizzie over for her).
As to another possibility for Lizzie, Maximilian of Austria expressed interest in her as a second wife OTL. She's born in '65, so a marriage won't be happening before 1480, but Maximilian would be more likely to take one of the OTL proposed matches with either England (Lizzie) or Sophia of Poland than some random princess of Saxe-Lauenburg.
Margarethe of Burgundy has been replaced by Elizabeth of Burgundy in the position of future-Queen of France. Elizabeth, now set aside, was too late to marry Maximilian of Austria, who, for lack of any better options married the Saxon girl. So, in the regency years, with her mother worried about the lack of available Kings, she married the Duke of Savoy. Anne of Brittany has been born here, and around 1490 Elizabeth of Burgundy would be set aside for her with Charles VIII, leaving her free to probably marry Juan of Asturias. Margarethe was also betrothed to the King of France because Burgundy was a better ally OTL, due to proximity and their already strong relations with Spain, both of which apply here. The betrothal to Elizabeth of Burgundy also causes cracks in the Anglo/Burgundy alliance, which helps France a great deal.
Matches, betrothals and children as of 1487:
Richard Plantagenet, Duke of Gloucester (b.1452) m. Mary de Valois-Burgundy, Duchess of Burgundy, Brabant, Limburg, Lothier, Luxemburg and Guelders; the Margravine of Namur; the Countess Palatine of Burgundy; the Countess of Artois, Flanders, Charolais, Hainaut, Holland, Zeeland and Zutphen (b.1457) (a)
1a) Elizabeth of Burgundy (b.1474) b. Charles de Valois, VIII of France (b.1470)
2a) Charles of Burgundy, Heir to the Duchies of Burgundy, Brabant, Limburg, Lothier, Luxemburg and Guelders; the Margraves of Namur; the County Palatine of Burgundy; the Counties of Artois, Flanders, Charolais, Hainaut, Holland, Zeeland and Zutphen (b.1478) b. Maria of Burgundy (b.1482)
3a) Francis of Burgundy, Heir to the Duchy of Gloucester (b.1482) b. Charlotte of Naples (b.1480)
4a) Margarethe of Burgundy (b.1486) b. James Stewart (b.1486)
Edward Plantagenet, IV of England, Lord of Ireland (b.1442: d.1483) m. Elizabeth Woodville (b.1437) (a)2a) Charles of Burgundy, Heir to the Duchies of Burgundy, Brabant, Limburg, Lothier, Luxemburg and Guelders; the Margraves of Namur; the County Palatine of Burgundy; the Counties of Artois, Flanders, Charolais, Hainaut, Holland, Zeeland and Zutphen (b.1478) b. Maria of Burgundy (b.1482)
3a) Francis of Burgundy, Heir to the Duchy of Gloucester (b.1482) b. Charlotte of Naples (b.1480)
4a) Margarethe of Burgundy (b.1486) b. James Stewart (b.1486)
1a) Elizabeth of York (b.1466) m. Charles I of Savoy, Duke of Savoy (b.1468) (a)
3a) Cecily of York (b.1469) m. James Stewart, Duke of Rothesay, Heir to the Kingdom of Scotland (b.1473) (a)
5a) Margaret of York (b.1472: d.1472)
6a) Richard Plantagenet, Duke of York and Norfolk (b.1473) m. Anne de Mowbray, Duchess of Norfolk (b.1472: d.1481) (a)
7a) Anne of York (b.1475) b. James Stewart, Duke of Ross (b.1476) (a)
8a) George Plantagenet, Duke of Bedford (b.1477: d.1479)
9a) Catherine of York (b.1479) b. Juan de Trastámara, Prince of Asturias and Girona (b.1478) (a)
10a) Bridget of York (b.1480)
Sir Richard Grey (b.1457: d.1487) m. Anne Neville (b.1456) (a)1a) Charles Edward Philibert of Savoy, Heir to the Duchy of Savoy (b.1487)
2a) Mary of York (b.1467: d.1482)
3a) Cecily of York (b.1469) m. James Stewart, Duke of Rothesay, Heir to the Kingdom of Scotland (b.1473) (a)
1a) James Stewart (b.1486)
4a) Edward Plantagenet, V of England, Lord of Ireland (b.1470) m. Isabella of Naples (b.1470) (a)
5a) Margaret of York (b.1472: d.1472)
6a) Richard Plantagenet, Duke of York and Norfolk (b.1473) m. Anne de Mowbray, Duchess of Norfolk (b.1472: d.1481) (a)
7a) Anne of York (b.1475) b. James Stewart, Duke of Ross (b.1476) (a)
8a) George Plantagenet, Duke of Bedford (b.1477: d.1479)
9a) Catherine of York (b.1479) b. Juan de Trastámara, Prince of Asturias and Girona (b.1478) (a)
10a) Bridget of York (b.1480)
1a) Edward Grey (b.1473) b. Anne St. Leger, Baroness de Ros (b.1476) (a)
2a) Richard Grey (b.1478) b. Muriel Howard (c.1480)
3a) Lionel Grey (b.1483)
Maximilian von Hapsburg, King of the Romans, Heir to the Archduchy of Austria, and the Duchies of Styria, Carinthia and Carniola (b.1459) m. Sophia of Saxe-Lauenburg (c.1460) (a)2a) Richard Grey (b.1478) b. Muriel Howard (c.1480)
3a) Lionel Grey (b.1483)
1a) Maximilian von Hapsburg (b.1476) b. Juana of Aragon (b.1479)/Anne of Brittany (b.1478)
2a) Eleanor von Hapsburg (b.1479)
3a) Frederick von Hapsburg (b.1483: d.1483)
2a) Eleanor von Hapsburg (b.1479)
3a) Frederick von Hapsburg (b.1483: d.1483)