Can i install eGPU on my laptop?

Yes you can install external graphics processing unit, but make sure it can be done by a network expert ( system support engineer ) .

Egpu or external graphics processing unit are few and far between, however the few you can get require a "express cardslot" on your laptop as this is the fastest interface on your laptop and the only one that can transfer video data fast enough to run games and programs
however if your laptop supports NVidia, s "mxm" or mobile express graphics then you can upgrade the existing MXM module to a faster module, however you need to check if your laptop can support it first
the best external graphics card in my experience is the "vidock"( http://www.villageinstruments.com/tiki-index.php?page=ViDock ) . However you will need a graphics card to install in the vidock and a monitor to connect the vidock to ( via any of the video outputs on the card of choice )
the vidock comes in three versions and each version supports a more powerful gpu… These are as follows:
ViDock 3 is designed to accommodate PCIe cards with no power connector.

ViDock 4 is designed to accommodate PCIe cards with one 6-pin power connector, or less power cards with no power connector.

ViDock 4 Plus is designed to accommodate PCIe cards with two 6-pin power connectors, or less power cards with one 6-pin connector, or with no connectors.

in summary the vidock is a excellent way to run games on a laptop not designed to run games, and although it won't come cheap it works well and is well worth the expense…
heres a video of the vidock in action ( using your exact laptop / g560 ) :

I hope this helps janith… Any questions let me know

If you have either an ExpressCard, mPCIe or more recently a Thunderbolt port on your laptop - chances are you can successfully implement an eGPU without much issue. The Lenovo g560 doesn't have any of those interfaces (I believe), so it will be technically involved and NOT cost effective to implement.

If it has a pci slot on the side then yes but this will cost a lot of money i would personally go to pcspecialist.co.uk and get a custom made laptop