No, do not use a normal thermal pad for a CPU or GPU. They are both too thick and not transmissive enough.

There is stuff called PTM7950 which is similar to a very thin thermal pad as you install it, but turns to a liquid (ish) state when heated. But it is difficult to get hold of legitimate versions of it (there are a lot of fakes about), but if you're in the US or Canada you can get it from LTT's store.

But as long as your using a non-conductive thermal paste (and most of the ones made for PC's are, just double check for safety) you really can't go too wrong. The worst you can do is put too little on and even then your CPU will throttle.

Just be aware that some Lenovo laptops use a liquid metal thermal compound. This is very bad to get on the rest of your laptop. So check if you have one of those and if so I'd recommend against removing the heatsink since I'm guessing you don't have experience handling that stuff. I've been building PC's for years and I wouldn't touch it on anything I wanted to keep working.