If a piece of Calcite (Calcium Carbonate) is put into the lake, would it dissolve?

If a piece of Calcite (Calcium Carbonate) is put into the lake, would it tend to dissolve?  Calcium carbonate solubility is 10^-8.35 M2, and the measured concentration of calcium ion is 0.1mM (millimolar)

Information received:
Lake pH=4, and total carbonate concentration of 0.001M.
Carbonate Equilibria:
CO2 + H20 <-> H2CO3  KH= 10^-1.5 mole/(liter.atm)
H2CO3 <-> HCO3- + H+   K1= 10^-6.3  mole/lter
HCO3- <-> CO3^-2  + H+  K2= 10^ -10.3  mole/liter

In a previous question I calculated the concentration of each carbonate species in the lake water, I think they are correct.  
H2CO3= 10^-5
HCO3-= 5.012 X 10^-8
CO3^-2= 2.512 X 10^-14

I do not not even know where to begin... my chemistry is a bit rusty.  Please help me setting the problem up