As far as I am aware, calcium lactate is preferred over say calcium chloride because as a food ingredient it imparts a very mild, bland flavour whereas calcium chloride at higher concentrations can give a noticeable salty/metallic taste.
Both CaCl2 and CaLactate have the effect of giving the dough a firmer texture (especially if other ingredients like milk proteins are added in the formulation) as the Ca2+ cation helps crosslink negatively charged polymers (casein proteins) to form a firmer network, which could help in trapping carbon dioxide air bubbles upon leavening during proofing and rising during baking. Calcium carbonate is sometimes used but can throw off balance of leavening agents since will react with acids to form carbon dioxide gas, and can impart an off flavour as well at higher concentrations. Calcium sulfate is rarely used since it has very poor solubility, but in some applications where a slow calcium release is needed it is ideal (eg. forming alginate gels slowly while in a food system).
Another example of this action by calcium is in vegetables cooked in boiling water. Often the pH of the water is alkaline so the vegetables stay a bright green colour (so magnesium will stay bound to chlorophyll and not turn to pheophytin which has a dull olive green colour). However, basic conditions also promote the softening of the vegetables, so calcium salts are also added to mitigate this and help firm the vegetables by crosslinking the negatively charged pectin polymers.
Another side benefit of using calcium lactate (since it is more expensive than calcium chloride) in the formulation, is that often there are other salts added such as sodium chloride, and if sold to food processors they may have limits set for maximum NaCl salt addition, and CaCl2 will increase the amount detected of NaCl since most QC labs doe Volhard/Mohr's titration with silver nitrate to detect amount of chlorides.