I was comparing its cast-style... as you well know.
Yes, Lulu is a support, but Glitterlance is not a "support ability". The official classification for "support" is anything that shields/heals an ally or scouts (although scouting is being phased out as a support mechanic). Glitterlance is an offensive spell on a support, not a support spell.
Allow me to refer to you the definition of a support:
"Support: Champions whose skills are meant to directly aid the rest of the team. They can either babysit a champion to make laning easier for them by providing healing, buffing allies, applying debuffs to the enemy team, or a combination of the above. The most common ability for a support champion is providing an ally with a shield of some kind. One of the main goals of a support is to let their lane partner farm minions for gold, as supports can buy key gold+ items to get gold for themselves, as well as controlling the map with wards, warding all key areas of the map. These champions usually rely on their skills more than their auto-attack."
Now, what does your champion do? Applies AD buffs, Grants allies on-hit effects and launches skillshots from then, has a massive AoE buff as an ult, and doesn't need gold to have fair stats and fill her role. This Sivir is a support.