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Roughly the same timeline as OP, except my LPP were completed Mar 2 and ceremony still not started
 
I am in similar boat. LPP completed Feb 22 & since then no update on Oath Ceremony. Niagara Falls office for test invite.
I am assuming everything complete except Oath means Decision Made has been done. From Decision Made to scheduling the applicant for a Oath slot taking this much time is completely beyond my comprehension.
 
For people above saying they've had LPP complete for a while: Have you tried emailing your processing office's oath ceremony team to ask for an oath date/update?