I have a new PC with Windows 10, but it doesn't recognize my external disk Lacie with serial number 1262811250271CR MOU2S2.
I have used the serial number on their official website and the website displays some user guides and software. This application doesn't appear there, but there are other replacements which means you might need to download and use those instead. However, being an external disk, there shouldn't be problems with the detection. Try downloading the apps and the installation guides available on the page.
Downloads: http://www.lacie.com/gb/en/support/mobile-storage/mobile-disk-usb-2/?sku=LAC301831
