Can you get body lice from the sand at the beach?

No, you can only get lice either from direct contact with a person that has them or by sharing personal items (e.g. combs, hairbrushes, cloths) with them.

Lice that fall off a person will rapidly starve to death and cannot be transferred.

What you are calling body lice are most likely the species of lice referred to as clothing lice, which actually live on the cloths but feed on the body underneath. The other two species are head lice and pubic lice.