Can using higher rated battery damage device?

I am in need of a battery for my Lenovo 3000 Y410 Laptop. It's installed battery has voltage rating of 10.8v. But the shop i've consulted has only a battery of 11.1v rating.

Should I buy the battery? I mean, Does using that battery can damage my laptop?

An answer with some good source from hardware vendor will be very much helpful. Please do not just put your opinion. Because I do not see any difference in your opinion and my opinion. My opinion is also "It is bad". But I need some reliable source.

Alright. So, I knew what I knew, but after reading and responding in here I wanted to break out the volt meter and test a few things. Just to be sure. But I'll get to that.

I've got a 2004 Toshiba Satellite A75 sitting up in the kitchen as the general purpose computer for me and the wife. I've got three batteries for it. Why? Well, I've got the original (still holds a charge) and two replacements for those times when I might be away from a power outlet but still might want to use it.

The Original Toshiba battery is 14.8v/6450mAh. The first replacement (I didn't purchase it) is a generic 14.8v/4400mAh. The replacement I did purchase is a RayOVac made 14.4v/6600mAh battery. It is sitting in the laptop at this moment, and is the battery I've used for more than a year now.

So, from personal experience I can say that using a battery with a slightly different voltage rating will NOT HARM YOUR LAPTOP. Heck, we are talking about running a laptop on a battery that puts out 14+ volts, that NORMALLY runs on 19 volts DC from the power adapter.

Oh, and all three batteries are designated as Li-ion

Now, as to the testing. I took a Li-ion battery from an LG phone... and the battery is designated as an LG battery (not a third party replacement) that is Li-ion and rated at 3.7v. It tested at 3.71v. So, I took a Li-ion battery from a Motorola phone. It was rated at 3.6v. It tested at 3.75v. Interesting. So, I took my stack of Li-ion batteries that I have for my Panasonic digital video camera. The one that came with it (printed as a Panasonic battery) is rated 3.6v, and tests as 4.09v. One of the replacements that is designated 3.7v tests at 4.11v. Another replacement designated at 3.7v tests at 4.03v

So, I checked the battery in the tester to make sure it was still good. Then I re-calibrated it. Then I tested a couple of DC power adapters just to be sure, and then rested all those same batteries. (Edit I also tested a mess of Alkaline AA batteries. We keep a stockpile of new ones for cameras, Xbox360 controllers, etc. All tested between 1.4 and 1.6 volts.)

So, again. What am I saying? I am saying there is NO problem with getting that battery. Provided that the battery casing was made for your laptop... meaning it will actually fit properly in your laptop. It is not going to hurt your laptop to use the 11.1v battery. I repeat. It is not going to hurt your laptop to use the 11.1v battery.