Does this laptop currently have an internal drive with a valid OS on it, or at the very least a local recovery partition? If so, then if it still can boot into macOS Lion, then you can download macOS 10.11 installer using the instructions in this Apple article, afterwards you can then upgrade to macOS 10.13:
How to download and install macOS - Apple Support
If you cannot boot into macOS on this laptop, then see if you can boot into Recovery Mode using Command + Option + R to access local recovery mode on the internal drive (theoretically this key sequence should not require you to authenticate with an AppleID whereas Command + R will). This should allow you to reinstall macOS Lion, although the installer's certificate has likely expired...in which case you will need to set the system date to an earlier year (not sure what year, maybe 2017, or maybe 2015).
Otherwise you have two options.
- Use the original OS X 10.6.x Snow Leopard restoration DVD which originally shipped with your laptop to reinstall macOS 10.6.x. You will need to erase the drive using Disk Utility in order to reinstall an older OS.
- If you have access to another Mac generally from 2007 to 2015, then you can use the instructions in the following Apple article to create a bootable macOS 10.11 El Capitan USB installer:
Create a bootable installer for macOS - Apple Support
If macOS 10.7 Lion was the highest version of macOS ever installed on this laptop, then you will most likely need to install macOS 10.11 El Capitan before being able to upgrade/install macOS 10.13 High Sierra which is the highest version of macOS compatible with a 2010 laptop.
After macOS 10.13 High Sierra has been installed, then computer will have an updated firmware which will give you access to the online macOS installers through Internet Recovery Mode using Command + Option + R (this key sequences behaves differently depending on the level of system firmware, hence why I mentioned Internet Recovery Mode here, but mentioned local recovery mode earlier which should bypass an authentication step).