Her final tweet on the topic read: "everyone try to kiss church members who are same sex as you they will so love it christmas comin early in kansas city~??????"
Lorde's tweets have since been deleted.
The Westboro Baptist Church rose to national recognition when it staged protests at a string of high-profile funerals declaring their "God Hates Fags" slogan, and was the subject of a Louis Theroux documentary entitled The Most Hated Family in America.
Based in Topeka, Kansas, it has also been criticised for broadcasting antisemitic and xenophobic views, and has picketed Ground Zero in the past.
Last year the church vowed to protest at a One Direction gig on the grounds that they were "crotch-grabbing little perverts". They also plan to picket a show by TV personality Kathy Griffin.
They have recorded a version of Lorde's No. 1 hit Royals that has had more than 4000 plays on Soundcloud.
Lorde recently sparred with Australian shock jock Kyle Sandilands after he queried the nature of her friendship with pop star Taylor Swift.
Her US tour has been well received by critics, with many dates selling out.
She has been forced to add more shows to her upcoming Australian tour due to fan demand.
Read more: Westboro church founder 'on edge of death'
- nzherald.co.nz with Independent