does dry ice sublimate faster in carbonated lemon lime soda, or cold tap water?

Answer 1

Possibly faster in cold tap water. The partial pressure of CO2 might shift the equilibrium of the sublimation of CO2 from the dry ice.
However...
On the other hand, both the dry ice and the soda are releasing CO2 to the atmosphere, where the partial pressure of CO2 and the total pressure is constant.

Therefore, I will say that (if water and soda are the same temperature and all things being otherwise equal) there will be no difference.