Same boat. My LPP were completed Aug 7th (updated in tracker the 9th). I think it depends on the IRCC office, my office is Montreal, my friend whose application also went through Montreal waited from getting LPP in April to his oath in July.LPP cleared on Aug 21. Still waiting for oath invite
I feel like if you don't get the oath scheduled within three days it'll take three months or more unfortunately.
Trying my best to be patient!