these are indeed good enough specs to run dota 2 and lol. i run dota 2 on a laptop with a core i3 and 520m, and it performs passably.
when you say lag, i wonder if you mean frame rate or actual server lag. if you are having network spikes and lag from input to onscreen action, you should run pingtest and see about the quality of your internet.
if you mean framerate, definitely you should be able to run these games on low settings at a fluid framerate, and if not, it may be that your cpu or gpu are throttled either through power options or because of excess heat. this is easily tested by running furmark. if furmark runs for 10-15 minutes and says that it's throttling, there's your problem, just clean out the innards really well.
if power options are set so that the gpu is turned off, or nvidia optimus is set this way, it's easily changed in your nvidia options. make sure lol and dota 2 are set to run with high performance gpu. this is the most likely culprit now that i think about it. right click desktop, nvidia control panel, manage 3d settings,program settings tab, select the programs from the list, or manually add, and there should be an option to make it use the gpu. also, in power options, make sure your laptop is not running at a low cpu speed to save power. a lot of them are set to do this when they are running unplugged. to test, run p95 or something similar while running realtemp, and make sure the speed is as advertised. if it's going at 1.699 or 1.79 that's fine, but if it's trying to save power it might be only going 800mhz, or .800 or so, and that would drop you some frames.
last but not least. there is the odd chance that you are running some bloatware, it being a new laptop, in the background. make sure nothing is running in the background that could overly tax your processor.
you definitely have more than enough ram, your friends are dead wrong about that. if your hard drive is breaking, it would simply take a long time to load, then run as normal.