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