Particles deformed by lattice is a useful feature. Especially for emitter particles with physics, that allows to easily define flows for particles with erratic movements.

Here for "none" particles supposed to stay sticked to surface, problem can be avoïded by changing modifiers order and by using lattice modifier before particles one.

You are right. You are describing a useful tip that does not correspond to a logical behaviour of modifier.

It would be consistent to add a particle icon to modifiers header to enable and disable modifier effect on particles.
But it is an UI lack that is not really blocking.
So, it should have a low priority status.

I like the idea to add slider for the particles. It is quite usefull, when you want to give an offset for origin of the particle object to put it below/above emitter's face.