Summary of conclusions:
It seems likely that known concentrated lithium deposits will not be sufficient to permit the transition to solar over the next decade or two, but there is plenty of lithium in seawater and other, less-concentrated deposits to permit such a transition. New extraction technologies will be needed if lithium batteries are to bridge the intermittency gap. Alternatively, some of the other utility-scale storage technologies might be developed.
However, independent of the above, your assertion, "Generating another 500 MW of solar energy doesn't actually represent any decarbonization if that energy is produced when demand is already saturated," is also incorrect. Generating another 500 MW of solar energy to satisfy demand currently being satisfied by coal, oil, or gas allows us to turn off coal, oil, and especially gas plants more often, which does actually represent decarbonization. It's only during hours when 100% of demand is being satisfied by solar energy that generating another 500 MW of solar energy doesn't represent decarbonization — and then only until utility-scale storage or demand response can suck up the zero-marginal-cost energy. Or until carbon emissions are net negative, of course.
It's quite plausible for demand response (e.g., charging your Tesla or freezing water in your refrigerator when the sun is shining) to play a bigger part in this than utility-scale energy storage, due to the much lower incremental costs. But my calculations linked above show that there is ample lithium in seawater to do it purely with utility-scale battery storage facilities, even without falling back to pumped storage, demand response, trains full of concrete, compressed-air caverns, etc.
Calculemus.