I have a couple of suggestions for you, which should be perfect for your needs.
For under $600, finding a laptop to handle light gaming wasn't too difficult. However, if you want a laptop with the best value (http
/www.amazon.com/Acer-Aspire-V3-572G-587W-15-6-Inch-Platinum/dp/B00K81O3PY/ref=sr_1_1?s=pc&ie=UTF8&qid=undefined&sr=1-1&keywords=laptop+840m). It costs $649.99, but it has a 840M, which will handle LoL and D3 nicely at medium/high settings.
If you want to stay under $600, the best I could find was an AMD Acer with an integrated GPU (hhttp
/www.amazon.com/Acer-V5-552P-X617-15-6-Inch-Touchscreen-Accelerated/dp/B00FS4UNG4/ref=sr_1_5?s=pc&rps=1&ie=UTF8&qid=1410221202&sr=1-5&keywords=laptop), which should handle LoL at medium settings.
Let me know if you have any questions!