It would help to know what type and age of computer it is, what OS it had originally and why you erased it. Perhaps you had dallied with a beta of ML and now want to rationalise your system?
Lion and ML have different Recovery Partitions, so it is not possible to go from one to the other without doing a complete erase, of the recovery partitions as well, from an external disk.
If you managed to purchase ML from MAS on the other computer, you can download a copy of the full 10.8.3 installer (4.4Gb) from the "Purchases" tab. It will download to the Applications folder and then ask if you want to install it on that machine. Make a copy of the Application and put it somewhere else. It will delete if allowed to run.
I'm not sure if you can just link two computers together and use one to do an erase install on the other, but some one will know. Else, I would buy an external hard disk, link it to the other computer and install onto it. Copy the full installer across too.
Now do an erase install on your own computer. Afterward you can use this external disk as your backup, using Carbon Copy Cloner (CCC) to keep it up-to-date.
What version of the OS did it ship with?
If Lion, and your Mac is capable of Internet Recovery, then you can reinstall Lion from Internet Recovery. Hold down Cmd-Opt-R on restart. You should see a spinning Earth and progress bar as it boots.
If you just booted into Recovery HD, then it will only offer to reinstall the most current OS on your Mac, which would be Mountain Lion.
If it shipped with Snow Leopard, then you may have to use that disk to completely erase the hard drive by partitioning it into 1 partition from the Partition tab of Disk Utility on the Snow Leopard Install disk.
Then, install Snow Leopard, update it to 10.6.8, then go to the App Store, Purchases tab, and download the Lion installer.