How does Tricyclic Antidepressant cause dry eyes? Does it cause melbomian gland or lacrimal gland to malfunction?

No. The lacrimal & salivary glands are innervated & stimulated to secrete by cholinergic neurons, ie they use the neurotransmitter acetylcholine (ACh). In medicalese we say that TCAs reversibly combine with & competitively inhibit the postsynaptic muscarinic ACh receptor. Simply put, they block the effect of ACh on the glands. Dry eyes & mouth are called "anticholinergic side effects."