Please help me - What should i change in my PC ?

It's possible that your HDD's are not fast enough, too; you could try defragmenting first.

Gaming PC? dis?

What games are you lagging in?

First generation i7 and HD 6800 series still qualifies as gaming PC, it's just not the latest and greatest.

My brother runs most games just fine on Phenom II X6 and HD 6850.

As for your problem, you'll have to be more specific than "lags a little". What game, what resolution, what settings, in what situations, etc.

It depends what HD 6800 series card it is. It could be HD 6850 or HD 6870, which are beast and should run pretty much anything maxed out at 720-1080p. However, there's a chance of it being some integrated garbage card, like HD 6810D (if I'm correct that's one of the 6800 series integrated cards).

TL;DR - find specifically which card you have, not just the series.

Look at the 7870 XT. Close to a 7950, but cheaper.

Graphics card, change to Nvidia GTX 670 or GTX 680... max the resolution, ultra settings, with smooth gameplay and zero lag :D
However, probably overkill for the rest of the system.

Consider replacing CPU and Motherboard for an 3rd Generation (Ivy Bridge).

What do you mean by 'lags a little'?

Are you trying to play it on max settings? Consider lowering the rez to 1080p.

Are you running max AA? Lower it to 2x or 4x.

Is the FPS dropping suddenly to 5fps for a few seconds before recovering? Your VRAM may be filling up. Make sure a video card upgrade includes more VRAM.

Is the FPS suffering from microstutter? Consider VSYNC, or lower some settings to the point where your FPS is high enough that you don't notice the FPS drops as much.

To further diagnose what's going on, play with GPU-Z running and see how much VRAM you're using. Watch your GPU Load to see if your GPU is even being fully utilised.

If your GPU is fine, your CPU may be the issue. Run CPU-Z and watch your CPU load across all cores. Is the game taxing one core, leaving the rest untouched? If it is, make sure any CPU upgrades run at higher clock speeds instead of just adding additional cores. 2.93GHz isn't exactly a fast clock speed these days, but is fast enough if the game makes good use of more than two cores.

Watch your RAM usage. Is your RAM filling up? Get another 8 gigabytes, your motherboard can hold 16.

What exact 6800 series is your card? 6850, or 6870? Either way, if your GPU is maxed out already, consider bumping up to a GTX 670 or a Radeon HD 7950.

Without knowing what settings you're running Tomb Raider 2013 at, we can only make inaccurate guesses.

That 6800 is not too bad, but depends on the version.

That said, I'm still using a factory overclocked GTX 275 and I can run most things.
I've been delaying an upgrade for a long time.

Delaying upgrades for 5 years now, Intel Core 2 Duo E8400 paired with a nVIDIA GeForce 9800 GT. nVIDIA GeForce GTX 650 Ti Boost Edition for 150 USD is going to be this years nVIDIA GeForce 9800 GT for best bang for the buck. Not, when will nVIDIA or AMD release their top of the line graphics card for under 200 USD again

While you're at it you can get yourself a real soundcard. Even a >10 years old SB Live is worlds better than anything that's integrated on a mobo (I mean stuff that's not interpretable as numbers, like a real hardware mixer). In the past I remember I had slowdowns because the integrated sound chip couldn't keep up - maybe that's your problem too.

Your OS is 32 bit? I guess you need 64 bit with these parts.

Well, as some pointed out, basically you should look at your video card and the motherboard.
The point with the motherboard is that it's a platform for every single component. If you get a better motherboard, the chances of overheating ar low so you will get a performance plus. Best motherboard are those designed to be overcloacked since they support higher voltages and implicitly temperature and also they give you more upgrade options.

When it comes to lagging and low game performance, the situation is a little bit different.
Update your drivers. Usually, video & chipset drivers can be easily updated by installing the new version. Don't know about AMD but nVidia also has an clean install option.

But this could be cause be almost every single component and piece of software you have.

For example, a mechanical HDD will (1) get hot and (2) allow fragmentation (actually SSD also do this but it doesn't matter there).
So make sure you degrag your system periodically.

When it comes to memory, frequency matters. In some cases, it matters more than the total amount of memory you have.
A 800MHz memory module is less efficient than a 1033 module. Also, memory is used to store data so that the system be able to run it faster. Since the data comes from the HDD, the higher the fragmentation is, the lower the process is, especially since the system also needs to handle the virtual memory.

When it comes to software, keep in mind that the software also runs in RAM and RAM allows fragmentation. Make sure you don't have unnecessary programs in startup and close programs such as web browser when playing (from my own experience, a browser with 20 tabs opened will seriously decease performance).

The CPU is fine, doesn't need an upgrade soon :))

As for your system, I can bet it's a software problem. The video card might use an upgrade I guess.
My system (ASUS Striker II Formula, Intel Core2Quad Q9300 2.55Ghz, ASUS GeForce 295GTX 1Gb DDR3, 8Gb DDR2 800Mhz) is 4 & 1/2 years old and I never had problems playing anything on 30+ FPS on less than max settings (i get 45 in FC3 on Ultra).

I'd say it's a case of poor maintenance as opposed to needing upgrades.

the motherboard is a lga 1156. not much to upgrade with. you can upgrade the hard drives to SSD's for a slight boost but thats it. you will need to upgrade the motherboard, cpu and ram and reuse the old parts.