Those cantrips are right. The 2 warlock class cantrips are Eldritch Blast and Green-Flame Blade. Light and Sacred Flame come from the Undying Light patron in UA: Underdark Characters from the Radiant Soul feature. Don't mistake that for the Undying patron in SCAG. Dancing Lights comes from the Drow racial spellcasting. Patron-specific spells are not automatically granted like domain spells. They are additional options that a warlock could choose to learn, so they don't automatically go on the sheet. Undying Light gains Burning Hands as a level 1 choice, and the patron only has 1 available patron spell per spell level up to 5th. That patron for a drow is an odd-couple pairing.
He picked GFB because it's a fire cantrip. Undying Light grants Charisma to radiant and fire spells at level 1 via Radiant Soul, similar to the Draconic sorcerer/Evoker wizard at 6/10. He was likely gearing up for Pact of the Blade since the pact weapon could be formed as a rapier and that Dex would provide decent AC with Armor of Shadows. Before the pact, he was going to use the dagger for it, which is a finesse weapon. An Undying Light Pact of the Blade Warlock by level 12 can stack Charisma to a single melee hit twice with GFB and then get Charisma to a secondary target as well. RAW, the feature lets GFB add Charisma twice to the 2nd target, though RAI it works like the sorcerer/wizard features on only a single roll of a spell. Additionally, Undying Light's level 6 feature Searing Vengeance is most effective in close-range and somewhat helps out with a Blade warlock's inherent softness.
What you already have there would make a fine multiclass into sorcerer. You could double up on charisma to fire spells via Draconic sorcerer. Undying Light is also very effective with a paladin multiclass but the character's low Strength holds that one back. It works just fine solo-classed too. You know what you're getting into if you continue into Pact of the Blade. Pact of the Tome would be a lot less risky and you could grab Shillelagh so the GFB tricks work well without having to be your main trick.