Struggled to find some info so I thought I would share my trip here. If you want to head to Siavonga and/or Lake Kariba from Lusaka, you can catch a minibus from City Market bus terminal in Lusaka. It passes by Chirundu border before heading back south towards Siavonga. Costs 75 kwacha and takes about 3.5h. We negotiated with the driver for a drop-off at the Kariba border post, otherwise it heads directly to Siavonga town. From the border post you can walk over the Dam and enter Zimbabwe before catching a taxi to the lake.