Q: Reinstall OS after replace Hard Disk

Yes, maybe. try command, option and R for internet recovery, or find Snow Leopard install DVD (general one). Don't try to use grey  original dvd's that came with another macbook, may not work too well. you can make bootable usb stick from here. Lion is no longer available in the app store, which is where you might get the OS from. You could get El Capitan though, maybe sierra. You need the Apple ID so it can login to the app store and try to get Lion for you, no Apple ID, no Lion-it has to authenticate your request. Just that simple. here you can find info on making a bootable USB stick for your old macbook

http://diskmakerx.com/

and here

http://osxdaily.com/2011/07/08/make-a-bootable-mac-os-x-10-7-lion-installer-from -a-usb-flash-drive/