Sorry that you had to visit confused.com
OK let us take it step by step:-
First, the innervation of the lacrimal gland is through the lacrimal nerve, a branch of the ophthalmic division of the trigeminal nerve (Vth cranial nerve - this is a purely sensory nerve, so the autonomic [sympathetic and parasympathetic] fibres running in the lacrimal nerve cannot be of trigeminal nerve origin as these are, of course, efferent fibres i.e. going away from the central nervous system (CNS); they come from the facial nerve (VIIth cranial nerve) via certain ganglia e.g. the pterygopalatine ganglion) - if you need more detail on anatomy, please IM me.
The parasympathetic fibres to the lacrimal gland comprise the majority of fibres; they stimulate the formation and release of the aqueous component (water) of the tear film.
The sympathetic fibres mediate vasoconstriction of the blood vessels of the gland. When less sympathetic impulses reach the gland, there is relative vasodilation, which means increased blood flow, hence increased tear secretion - this is inter-related to the
psychologically based phenomenon of crying (I have some tissues in my pocket if you need one! - sorry!).
The sensory fibres are intrinsic to the trigeminal nerve and do what they do elsewhere in the body i.e. mediate sensations of pain, pressure, temperature, etc. from the gland (when required by external/internal stimuli) to the brain for perception of sensation.
I hope this helps!
PS. If still shedding tears, listen to "Three Little Birds" by Bob Marley [ask dad or mum who that was!] - it will steer you readily towards smiling!