You won't have a chance of getting a laptop with a dedicated graphics card for that except on places like eBay, if you want to buy from a retailer I would go refurbished because of the amount and then just go for the best processor you can get and by extension best integrated graphics, try something like this
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I can't promise it won't still lag, it will be better though.
The best option if possible is to either get one on finance (only if you get 0%apr or can get a credit card with 0%apr for long enough that you can pay it off) or just save up till you have a better amount to spend I personally wouldn't spend less than $800 on a gaming laptop but I live in England and stuff is alot more expensive over her so you could probably find an ok one for around $550