Lux isn't a burst mage

Riot said she's a burst mage with elements of artillery, possibly the other way around.

I think what made them consider her a burst mage first are the fairly long cooldowns on her Q and E, her iconic combo of Q and/or E into R to delete carries, and the bonus damage she gets from firing auto attacks. A true artillery mage doesn't have very long cooldowns on their poke spells (Xerath has 5 seconds on Q, Ziggs has 4 seconds on bouncing bomb compared to Lux's 10 seconds on Lucent Singularity) and wants to just keep peppering the enemy to wear them down at low risk while a burst mage is fishing to fire their full combo and delete someone, and if they spend one of their cooldowns frivolously they become very vulnerable for a good while.

Zed is not a assassin

he is a mobile, marksman killer

Yeah, she is. Lux is Mage whose kit is designed to do burst damage, i.e. a burst mage. Nothing in that link matters.

Who cares that Riot put out yet another post of arbitrary titles for champions that have no effect on how the game functions? It's just as pointless an exercise and a waste of Riot's time as the last times, like where they tried to convince everyone to start calling ADCs "marksmen" and to call one too.

i think she has the range, but not the cooldowns to count as artillery mage.

like ziggs can basically constantly spam his q. xerath aswell.