MMB is often hopelessly wrong on lounge access (c.f. How many people see they have Concorde Room access)

Formally, I don't think you'll have access at MAN, because your connection is the next day, and will be after 6am. By all means do enquire tho, as I expect you will.

The return case should be no concern, simply show your inbound business class BP at LHR, they should be very very familiar with this scenario.