Can modem/router or internet cause computer to lag?

[Ryou-kun]

I am aware this is a stupid question. I really need to confirm it.

 

It is about my cousin.

Several days ago, he told me his computer was lagging so bad and randomly get BSOD.

Few days later, he told me he fixed it because his Logitech G Pro Wireless mouse was low on battery, so he charge it and fixed it.

After that, he told me it might have been his modem/router that caused his computer to slow. 

Lastly, he recently told me Spectrum guy came and fixed his internet. No more lag.

 

I am pretty sure modem/router or internet doesn't cause computer to lag, right?