AD's can as previously mentioned can/may cause Manic/ mixed episodes.
Im going to assume the Lithium dose you posted is incorrect, as its typical in 300mg doses.
Does your family member see a Therapist? If not it would be wise for him to, It can help process thoughts and feelings.
Being on Benzos and sleeping meds can actually cause depression as they are depressants. So maybe that is causing some of the problems.. just a thought.... he should discuss with his Pdoc.
If your family member talks about suicide.. please take it serious.. the old " if people are really suicidal they don't talk about it" is pure and utter bullshyt.
I hope he gets the help he needs to enjoy life.
Welcome to PC