144hz would be good but not a must and please cheap
Do you have good internet there?
Wlan just like that
What is your definition of "cheap"?
Do you have a certain maximum price?
LoL runs on every toaster. A laptop is enough for 300 euro. But if you want a little more, there are laptops with a GTX 1650 to GTX 1660 MaxQ with an i5 in the price range around 800 euro. This means that other games can also be played quite well in 1080p.
Do you have a link from a sufficient laptop mfg
Max 500 would be good
There are a lot of models from different manufacturers with similar hardware. But here are a few.
https://www.notebooksbilliger.de/...635+673576
You would have to get Windows to do this.
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https://www.notebooksbilliger.de/...100+673586
You have a 144Hz display
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https://www.notebooksbilliger.de/...304+673570
And here something decent with GTX 1660Ti, 16GB RAM and AMD Ryzen 5. Games like Warzone also run without problems.