The Henry Tayali Gallery is Lusaka's closest thing to a national contemporary art gallery, run through the Zambia National Visual Arts Council at the Showgrounds. It is named for Henry Tayali, one of Zambia's most important modern artists, and shows work by local painters, sculptors, and mixed-media artists.
The space is modest, but that is part of its value: you are seeing the city's active art scene rather than a frozen national collection. Exhibitions change, so call or check social channels before going if your time is tight.