Many aquarium plants require CO2 injection to be grown in an aquarium. However clearly these plants get an adequate amount of CO2 when they grow immersed in lakes. Are the CO2 levels higher in the lakes in which such plants live? If so, why? And why can it not be replicated in an aquarium?

One thought I had was that lakes have a higher surface area to volume ratio than an aquarium so CO2 dissolves more rapidly into them.

I also understand that decomposition produces CO2 in a lake, but surely this process occurs in aquariums too if the aquarium consists of a capped soil substrate layer and is well cycled. I also understand that CO2 is produced by the organisms in a lake - but I also can't see how the level of CO2 produced by organisms per litre would be less in an aquarium.