So I got this website with 2,5-3k uniques a day.
With about 12-15k registerd ad showings a day and a 0,04 ctr

Its a league of legends website, where users gets directly transfered from a LoL facebook group.
I have one 300x250 top right, one 300x250 middle right and one 728x90 on the bot of the page.

Why do I only make 1-3 dollars a day?
How can I make more?

your traffic seems young, and has a short attention span so that is a tough demographic to earn from.
how long do they stay on your site?
having a 728 x 90 on the bottom is no good, move it to the top of your page where it will actually get exposure.

You're making what, about $0.7-$1 Page RPM then? Doesn't seem to bad for something in a "crappy" niche... I am sure you can bring it up to $1.5 RPM and maybe even $2 with perfect ad placement, but that's about it, I reckon. I have always found sticking 1 ad on the top, 1 sky skraper type ad in a good location on the right, if you have a widget/menu area there, and then 1 ad in the middle of the text works quite well. If you are using WP, there are plugins that will insert ad boards in the middle of the post.

Swap the 300x250 for a 300x600 an have the 728x90 with a bit of that 300x600 above the fold. Also make the some targetable segments. Use text and image also.

You're in the wrong niche for adsense, i wouldn't expect much earnings off the gamer croud as they are usually ad blind and have adblock installed.

Gaming is a small CPC Advertising Niche with pretty much every Ad being either related o the user (and users have for clever) or a bloody World of Warcraft Ad, which by the way 90% of League of Legends users hate WoW & Blizzard (who make WoW).

I'd suggest working on your Site to gain more traffic etc.. Before looking at advertising, if you get a nicely sized & active form you can sell Ads via BuySellAds (Need about 200,000 Uniques & a large enough User base - just keep building your forum) You could also offer upgrades to members to get them a special pass or something, as well as accept donations (I know forums/gaming communities that have made $400/Month from Donations)

don't use adsense for a game website. try something like ad4game.com I tried them on a small game website i used to run and they average $5/1K hits.