Very, very unlikely, as in you will never see it happen. At usual pool pH and TA calcium carbonate saturation occurs with the CH at roughly 300 ppm. With lithium carbonate being 1000 times more soluble, you'd have to get your lithium levels to the 300,000 ppm range (in calcium carbonate weight units) and as you know even using chlorinating liquid or bleach for years doesn't get the salt level anywhere near that high.
You need to think of lithium more like sodium than calcium. Compare the solubilities and solubility products in
this link where I list the carbonates in order of least to most soluble (sometimes solubility is higher than the solubility product implies due to ion pairs):
Mercury(I) Carbonate 0.000045 g/L solubility; K
SP 9.52x10
-15
Lead(II) Carbonate 0.0011 g/L solubility; K
SP 7.4x10
-14
Cobalt Carbonate K
SP 1.4x10
-13
Manganese(II) Carbonate K
SP 1.8x10
-11
Iron(II) Carbonate K
SP 3.2x10
-11
Copper(II) Carbonate K
SP 1.4x10
-10
Nickel(II) Carbonate K
SP 6.6x10
-9
Strontium Carbonate 0.01 g/L solubility; K
SP 4.59x10
-9
Zinc Carbonate 0.01 g/L solubility; K
SP 1.4x10
-11
Calcium Carbonate 0.014 g/L solubility; K
SP 2.8x10
-9
Barium Carbonate 0.02g/L solubility; K
SP 1.03x10
-8
Silver Carbonate 0.033 g/L solubility; K
SP 8.1x10
-12
Magnesium Carbonate 0.106 g/L solubility; K
SP 3.5x10
-8
Lithium Carbonate 15.4 g/L solubility; K
SP 2.5x10
-2
Sodium Carbonate 211 g/L solubility; K
SP 1.2
Potassium Carbonate 1120g/L solubility; K
SP 2130
Ammonium Carbonate 1000g/L solubility; K
SP 4520
You can see that magnesium carbonate is around 7-8 times more soluble than calcium carbonate which is why with most hard water you see calcium carbonate scale first. It's possible to have water high in magnesium and not calcium in which case you could get magnesium carbonate scale but that is unusual. You can see the very large jump in solubility going from magnesium to lithium. For practical purposes, you can consider lithium, sodium, and potassium carbonates to be very soluble in pool water at concentrations you could have in such pool water. You can also see that there are many metals that can precipitate with carbonate including zinc, nickel, copper, iron, manganese and cobalt, but metal ion concentrations are far lower so in practice you don't see zinc carbonate and for the other metals you're more likely to see oxides-hydroxides of those that are less soluble than the carbonates.