Although I have been aware of sponges in Lake Tanganyika for many years, I have not seen any information about them ever. I looked and looked for information when I received your question but could find nothing. I then thought perhaps the next best source might be people who have actually been to the Lake, and hoped that they could shed some light on this subject, and they did!
There are two or three types of different sponges found in Lake Tanganyika. The most common sponges are a thick flat mat attached to the large boulder type rocks found in the Lake. They are not collected, nor found to be of any value to anyone including natives. The fish do love them, and are found picking at them, retrieving algae and small crustaceans. Smaller sponges are found among the sandy shores.
There are many studies being performed on Salt Water sponges to determine how they protect themselves from predators. Hoping that someday their defense mechanisms will aid in research for medicine to cure many diseases. However, this does not seem to be the case for these freshwater sponges.
I did not know that sponges were also found in Lake Malawi. The sponges from this Lake are also found attached to the rocks, but many are in the surf and can be found along the sandy shores. They are small clumps about the half the size of your fist. Some have been brought home as souvenirs, but that is about it. They are not collected or used by the natives.
If you are interested in obtaining sponges from Lake Malawi or Lake Tanganyika you may have make the trip yourself! In the last couple of years there has been an attempt to sell rocks from Lake Malawi. However, you can imagine how much it would cost to have these rocks shipped in. If money is not an issue, you might consider getting some "Live Rock" from Lake Malawi, but there is no guarantee that there would be any sponges included.