GPU seems to heat to over 93C when playing Counter-Strike: Source (at 1600x900 resolution). After a while ThinkPad shuts down on its own. Should I lower my graphics settings? I tried that, but it didn't seem to What exactly should I lower?
First, do you have the T520 with the optimized graphics, the NVidia NVS 4200m? Because even if you do, it's not a gaming video chipset...
From Notebook Check.
Otherwise, that laptop comes with an Intel HD 3000 IGP.
Either way, the T520 isn't a gaming laptop. It doesn't matter if it meets the game specifications or not. It wasn't built for the punishment that games deliver. It is a business class laptop that was made to run in that type of environment, under that expected type of load.
Why is it overheating? As mentioned in the comments, the cooling channel might need to be cleaned... as in there might be a layer of dust and debris (like dryer lint will look like) between the internal fan and the heat sink. You might also be using the laptop on a soft surface, causing the fan intake to be blocked. For all we know, the original power adapter failed or was broken, and you have replaced it with a less-than-adequate power supply that is providing almost the wattage necessary.
There are multiple reasons why your laptop could be overheating, and we just don't know enough about your specific circumstances to be able to say exactly why. However, at the very least, using a business class laptop as a gaming laptop will make it run hotter than normal.