Delia wouldn't fit a lance because lances are too straight-forward while Delia is a dancer/acrobat.
Delia would Fit a lance Very well due to these facts
1. Knight Royalty: Delia is Royalty and built up to be the generic battle princess weapons generally used by Royalty in most fantasy instances are Lances or Rapiers
2. Gigantic Relationship: She canonically spent a long time with the Giants even eventually with Karok after she joined the crimson blades In Mabinogi lore a Giants "Ultimate weapon" is the Lance and given her relationship with Giants as well as her status as a Royal Knight and princess it's very likely from a character standard to use such a weapon
3. The idea for a lancer character has been floating around for awhile so it kind of hypes itself up a bit even before she gets released
That is why i believe Delia's second weapon will be a lance
However i honestly would prefer barehanded Martial Arts which also has a chance due to her relationship with Giants and would be nice to dropkick then full mount an enemy for an ult