Latent CAN BE contagious. Ever heard of "Typhoid Mary?" Same is true for many infectious diseases.
Latent simply means it's not visible, and causes no symptoms, at the time that it's latent' essentially hidden. If you're talking about latency, then you need to specify diseases you're talking about.
Cancer or the blood, pancreas, etc., can be latent, as can TB, diabetes, many deep fungal infections. That doesn't mean they're not going to kill you.
SPECIFIC CONDITIONS and how their latency can be manifested.
Also if it was a latent TB infection you need to take antibiotics for TB because it prevent spread throughout your own body. Usually, latent means you have been infected but it is dormant until you get lowered immunity.
I agree with CurfewX. Do you know which type of HTLV it was? HTLV I, II or III? Latent just means in this case that the person has the virus but hasn't yet gotten the disease. If it is Type I or II then they either had it before or could potentially get it. HTLV III is the old name for HIV. If you poke your finger with a dirty needle after drawing blood from that person there is a 1 in 1000 chance of getting HIV. But for the Type I it is probably less and dependent on how good the persons immune system was at the time. We have cancer cells in our body all the time and don't get cancer. If our immune system is good it can fight and remove the virus or other foreign agent. But some things are more infectious than others. So, yes best to get more information. If worried about HIV get the 4th or 5th generation HIV test about 28-30 days after being affected. Then that would clear that one up. I think there might be a molecular test for the other two. But, not sure. As mentioned above talk to a doctor such as an infectious disease specialist.
It means it's not infectious at the moment. Can you add more details to help us give you a complete answer?