Recently my brother asked me a question and I didn't know how to answer. He told me its people informed him that its mustahab to do latem without a shirt. I personally think its unchaste even if its at an all men mosque. I've never heard of this before so I would like to know if it is Mustahab, makruh, haram, or just something some people culturally do with no basis in hadith?

There is no specific recommendation to observe latom without a shirt. What is recommended is to show grief and sorrow for Imam Hussain’s (a) tragedy. If some men genuinely feel that they are showing their support for Imam Hussain (a) in this manner, then it’s fine there is nothing haram about it. If some feel it is immodest or unusual, then they can express their sorrow in a different setting.