First, which model ? x200/x201 or x220 ?
I assume since you need fan service, its been at least 2-3 years old. I actually just did the quick fix on 2 laptops here.. both had clicking fan the bottom gets heated.
The better way is to remove the whole motherboard, take the fan and open it to clean it and use a better lube. If your fan is just loud and you want a quick fix, all you need is the keyboard off, vacuum the dirt out . I have these machine oil with long spout. I can put the laptop on the side and drip oil into the fan assembly, spin it a little and quick fix is done.
This is what I use. I'm sure its not the best type but its the only one that I can use without taking apart the whole laptophttp://www.bigpaintstore.com/wd4-10034.html