I can't speak for the Mormons, but I am a Lay Eucharistic Minister in the Episcopal Church. The term "lay" is actually a corruption of the more formal "laity" which distinguishes those of us who participate in the Eucharist (Holy Communion) from the ordained priests and deacons.
You are, of course, correct. The mormon usage of the term "lay" is merely to claim the ordained priests are unpaid. They can't say "volunteer" because they don't volunteer. However, to the extent they are not really trained as ministers or priests, they would not qualify in other religous groups. The lack of adequate training and reliance only on the Holy Ghost is, to say the least, ominous. They blunder away on inane interviews and bad advice.