One of the biggest problems for existing life in sub-surface Martian lakes is salinity. Hypersaline water is likely detrimental to the origin and continuation of life since high levels of these salts will negatively impact many organic reactions (and interactions) critical to abiogenesis, and in any living organisms which might arise. The primary elements of these salts are Na+, K+, Mg++, Ca++ and Cl-. At low concentrations, as seen in seawater on earth. they are useful in various activities, such as enhancing reactions, and creating membrane potentials which drive metabolites into cells, etc. But at higher concentrations, they would begin to interfere, and even degrade chemicals and structures, rendering such an environment unsuitable for life.
On earth, very few life forms can survive in hypersaline waters. Brine shrimp are a classic example. But the vast majority of life on earth would perish in hypersaline conditions. Which is why salts are used as preservatives, such as salted pork and salted fish. And there are plenty of salts in the soils of earth, and plenty of "fresh water" lakes. Clearly the presence of salts in the soil does not mean that all lakes will be hypersaline. It would depend a lot on hydrology and the surrounding soils. It seems unlikely there would be lakes with low salt content on Mars without some means of moderating excessive salt content. This is prevented on earth by an active hydrology, where rain can continuously maintain lower levels of salt in lakes and rivers, for example. Such mechanisms on Mars would appear required to allow for lower levels of salts in sub-surface waters, and allow life to arise and survive. Of course an energy source is an entirely different issue.