So, to summarise:
FCL.700 makes it clear that a LAPL holder does not need to have a class rating. This is because a LAPL is, by definition, restricted to SEP of 2000kg of less.
Because of this the requirements of FCL.740 do not apply. If you don't have a class rating, there is no validity period attached to it.
So, only FCL.140.A applies. Simple really...