To fix this, you need to change a setting in your BIOS. Windows XP is an older system that doesn't natively recognize modern SATA hard drives without extra drivers. Since you can't find the specific driver files to put on a floppy disk or USB, the easiest solution is to tell the laptop to act like an older machine.
Restart your ThinkPad and press F1 to enter the BIOS. Go to the Config menu, select Serial ATA (SATA), and change the mode from "AHCI" to "Compatibility." Save and exit. Now, your Windows XP disc will see the hard drive normally. Once the installation is finished, Ome TV, you can install the Intel Matrix Storage drivers from Lenovo's archive if you wish to switch back to AHCI mode.