A couple Lutheran prayer books jump to mind; I'm not sure that any of them are exactly like the BCP, but they're similar.
EmmanuelPress sells "
The Brotherhood Prayer Book." I don't have a copy of it (but I have used the
online version), but I believe it has the canonical offices for each day of the year in Gregorian chant. I really want a copy of it, but I would prefer them to use ESV instead of KJV since that's what the LCMS tends to use, so that's why I've held off.
Concordia Publishing House also sells a few different prayer books:
The Treasury of Daily Prayer is a phenomenal resource. It contains daily lectionary readings, psalms, chant tones, daily prayers, and a meditation/sermon excerpt/etc. for each day (usually from a Church Father or Old Lutheran)
Lutheran Book of Prayer is pretty good. It has morning and evening prayers for each day of the week on a 4 week cycle (so 28 morning and 28 evening prayers total), as well as prayers for various occasions: preparation before the liturgy, in times of struggle or sickness, for family members, etc.
Starck's Prayer Book is supposed to be great as well. I have never used it, but it has been recommended to me by a few people. I'm not sure how it compares to BCP.
My bet is that the closest equivalent to BCP for Lutherans would be the Brotherhood Prayer Book or the Treasury of Daily Prayer.