As per Lonely Planet discussion thread, only currency that can be withdrawn in Zambia is Zambian Kwacha.
If you have make payment in USD, then either carry the cash in USD or withdraw money in Zambian Kwacha and buy USD from the banks.
In case you decide to carry cash in USD, keep in mind few things (quoting from the above link) -
- All USD must be new editions (2006 for some denominations and 2009 for others). No creases, no marks.
- Carry large denominations ($50 and $100) as they can only be changed as the exchange bureau
- All ATMs accept Visa cards, but most don't accept your Master Card
And also there was a ruling in June 2012 that companies are not allowed to deal in USD and can only accept the local currency Kwacha. So check with the places where you were asked to pay in USD once again, they might ask you to pay in Kwacha after this ruling.
PS: Zambia is changing its currency in January 2013 and dividing their currency by 1000