OS X Lion reinstallation - Missing recovery system

Network Install of Lion Through Yosemite

Be sure you backup your files.

1. Restart the computer and after the chime press and hold down the COMMAND-OPTION- R keys until a globe appears. Wait patiently - 5-15 minutes - until the Utility Menu appears.
2. Select Disk Utility from the Utility Menu and click on the Continue button.
3. After Disk Utility loads select the drive (usually, this is the out-dented entry with the mfgr.'s ID and size) from the side list. Click on the Partition tab in Disk Utility’s main window.
4. Under the Volume Scheme heading set the number of partitions to one volume. Click on the Options button, set the partition scheme to GUID then click on the OK button. Set the Format type to Mac OS Extended (Journaled.) Click on the Partition button and wait for the process to finish. Quit Disk Utility and return to the Utility Menu.
5. Select Reinstall OS X from the Utility Menu and click on the Install button.

According to Disk Utility, the partitions on your drive are encrypted. So, I would either turn off the encryption using Security & Privacy preferences or re-partition and reformat your drive. That is the reason for the use of Network Restore. Just be sure you select the out-dented disk entry, not an indented volume entry.

It's difficult for me to provide the correct guidance without an image of what your are seeing in Disk Utility. If you could take a snapshot and post it here that would be a big help. The only ones I have are from El Capitan. The network one is an older version and looks different.

Changes in Disk Utility in El Capitan.

Disk Utility is somewhat different in usage if you need to partition, re-partition, or format a disk for use with your Mac. Please read these instructions if you are using El Capitan.

1. Restart the computer and after the chime press and hold down the COMMAND and R keys until the menu screen appears. Select Disk Utility from the main menu and click on the Continue button.
2. After Disk Utility loads select the indented volume you wish to partition and/or erase from the left side list. Click on the Partition or Erase icon in the Disk Utility toolbar. The Partition icon may be grayed out if the device has never been partitioned for the Mac. If this is the case, then you need to select the out-dented physical disk entry in the sidebar.
3. If the Partition icon is not active, then select the out-dented entry as mentioned above. Click on the Erase icon in the toolbar. A panel will dropdown in which you can select the partition scheme - GUID - and the Format type - Mac OS Extended, Journaled - from two dropdown menus. If the disk has been partitioned, then you can erase it by just selecting the Erase icon in the toolbar. Set the format type to Mac OS Extended (Journaled) in the panel’s dropdown menu. In either case once configured you can click on the Erase button and wait until the process has completed.

As you can see in the image below what the out-dented and indented entries are in the sidebar. At the top is the toolbar. In this image, the Partition icon is active because the selected disk is already partitioned. The Erase icon is now inactive because no volume is selected to erase.

For more help with the new Disk Utility please see: Hands-on with Disk Utility in El Capitan.