When algae dies and decomposes, the bacteria that are the agents of decomposition cause severe oxygen depletion in the lake. Depending on the volume of algae, it can pose a risk to the fish population. Algae can block sunlight to the plants which are rooted to the bottom, decreasing their rate of photosynthesis and possibly leading to wide-spread die off. This adds to the amount of decaying organic matter, and further depletes the oxygen supply.
Extreme algae blooms can also pose a direct toxicological risk to aquatic (and even non-aquatic) life forms, though I am not acquainted with the chemical processes involved. I assume Google might have something to say on the matter.
So yes, algae can be a big deal. The Salton Sea in California has episodic algal blooms, and thousands of tons of tilapia and corvina wash up dead on the shores every year. Possum Kingdom lake in Texas had a really nasty kill a few years back, though it is well recovered at this point. Poor water quality due to excessive nutrient loads is largely to blame. The algal bloom further reduces the water quality, and it can cycle out of control.
Do research on eutrophication (the process of lake aging) and you will find eutrophication is accelerated in man-made reservoirs compared to natural lakes. It ties together nicely with nutrient-loading, algal blooms, and hypoxia. All in all nasty stuff.