Rush Grail, then situational. I've gone Haunting Guise for the health/mpen before (Liandry's wouldn't be till 6 item kinda deal), Rylais for survivability.
Deathcap, Void, Athenes at some point.
So my basic build:
Boots 3 (Could do flask opening, but I feel too slow) -> Grail -> Athenes when you feel you want the CDR/full item.
For early health: Haunting Guise
For damage: Deathcap, Void
For later survivability: Rylais, Zhonyas
Haven't messed around with Deathfire yet.
Liandry's isn't the best on Syndra, due to the bursty nature of her skill set, though if you're poking with Q-W the slow means you get a double damage Liandry's burn which can work in a more pokey comp. The MPen from Haunting Guise and Sorc Boots is where its at though for damage.