You can use the 2011 MacBook Pro to download the Mac OS X Lion 10.7.5 install disk image.
Mac OS X Lion 10.7.5 is the last version of Mac OS X the 2006 MacBook can run.
Download OS X Lion from here, https://support.apple.com/kb/DL2077?viewlocale=en_US&locale=en_US
This will download InstallOSX.dmg to your Downloads folder.
Once downloaded open the InstallOSX.dmg to get the InstallOSX.pkg.
Double-click the InstallOSX.pkg and an installation window will open, this does not install OS X Lion
but creates the Install OS X Lion.app in your Applications folder.
Now download this free app, https://diskmakerx.com/download/
Scroll to the bottom of the page and click on the blue text DiskMaker X 3.0.4 (4.2MB)
Use this app to create a bootable USB flash drive installer, USB should be over 8GBs in size.
Open the DiskMaker app and follow the onscreen instructions.
When you have created the bootable installer plug it directly into the MacBook.
(The hard drive should have already been installed by now)
Restart your mac while pressing and holding down the option/ alt key.
In a minute or two you should see the StartUp Manager.
Select the USB and press Return.
The mac will now boot to the USB.
From the Utilities panel click on Disk Utility.
Highlight the Disk (usually called after the Disk manufacturer) and press Erase.
Give the Disk a name.
Format: Mac OS Extended (Journaled)
Scheme: GUID Partition Map.
Click Erase.
When Done quit Disk Utility.
Click On Install OS X, press Continue.
The installation procedure should start up follow the prompts.
If the installation of Mac OS X Lion does not go ahead it may be because the correct firmware is not
installed on the MacBook, this means you may have to install Mac OS X Snow Leopard 10.6 first.
Mac OS X Snow Leopard was only ever available as a DVD installer.
You will probably have to buy a second hand disk on the internet (unless you already have one)
make sure it is the official Apple retail version which came with a white cover and a white DVD.
To install Snow Leopard insert the DVD into the mac.
Power the mac on while keeping the C key pressed.
The mac will now boot to the DVD.
Follow the instructions for formatting and installing Snow Leopard.
The DVD will install either version 10.6.3 or 10.6.6 but you will need to install
the update to 10.6.8 before you can then upgrade to Mac OS X Lion.
Download the 10.6.8 update here, https://support.apple.com/kb/DL1399?viewlocale=en_US&locale=en_US
Once downloaded double-click to install.
Having upgraded the MacBook to Snow Leopard 10.6.8, open the App Store Updates page and check
for any available updates and install them.
Now you are ready to install Mac OS X Lion, using the instructions described above.