The issue with laptops is that in most cases, unless you are spending $1k then they don't even come with a dedicated graphics card in them at all anymore. The standard computer companies make more money selling over rated web surfing tools at jacked up prices to your grandmother than they do making budget gaming devices. As far as custom built is concerned, well it's just not cost effective for custom companies to build lap tops for less than $1k because of the fact that they sell fewer machines over all, though you would get more for your money from them.
While I think it would be really awesome of Riot to make an even lower graphics setting for those die hard fans that are just down on their luck, I think it also might not be cost effective for them.
Your best bet is going to be a second hand machine, check places like pawn shops and see if you can't cash in on someone else's misfortune. I nabbed an alright laptop at one that gets me 10-20 fps consistently at low settings on most everything, though I have models at high and effects at mid, but that's a personal choice and I avoid ranked games as to not drag down team mates. The thing only cost me $200.
Those of you demanding that anyone having issues run out and buy a new computer because they are ruining your fun, remember that this is a free to play game. You know what free to play games attract? People who don't have the disposable income that they can spend on toys. Toys like a computer powerful enough for modern games. If you think dropping $400 or more on a toy, and unless you somehow need the graphics power for your job then it is just a toy, is completely reasonable then consider yourself lucky. There have been times in my life when I've barely broken $1k a month, and I'll bet a lot of Riot's fan base have been in the same boat at one time or another. I consider myself blessed to be in a much better place in my life now.
So save up for a computer in the long term? When money is tight it can be hard to hold onto. Let's say you're 22 and fresh out of collage. Can't seem to get a job in your field yet so you work a couple part time jobs and make about $2k a month. Off the top that's going to be about $700-$800 for rent, $300-$400 for food, $50 for phone, $50 for internet, $80-$100 for power, $100-$150 for water, depending on where you live another $100-$200 for heat, depending on how much travel you have to do another $50-$150 for gas, $100 or more for car insurance, pay for your own health insurance then say goodbye to another $100 or more. So that's anywhere from about $1,630 to $2,100 just for what's considered your "must haves." Though you could forgo the internet, but then you wouldn't care about LoL at all. Oh, and if you've got some student loans to pay back, or any other debt from credit card mistakes, your bills can be much higher.
That's not counting any other expenditures, maybe you're a smoker or like to get a few beers on occasion. Maybe as a gamer you are interested in other nerd/geek activities or hobbies like miniatures or cosplay, all things that cost varying amounts of money. Or what about unforeseen events? Accidentally crush your glasses, destroy your transmission, bust a window, etc. Saving up $1k for a gaming lap top could take a full twelve months or more, and that's with only a little going wrong.
One of you mentioned that the future of gamers are the 21-35 crowd instead of the under 18s. Doesn't make much sense considering that that demographic is traditionally the poorest demo there is, as their adult sized paychecks come with adult sized bills but they haven't gotten themselves the promotions or raises to quite handle those bills yet.
Tl:dr Second hand computers aren't bad, try pawn shops but know your specs. If you don't care about the realities of the expenses of computer gaming, then I only have negative things to say to you.