No disk options when attempting to reinstall Mac OS X Lion

It sounds like a damaged directory. See my FAQ on data recovery:

My data has become inaccessible, and I don't have a backup!

Also note, the Internet Recovery may not work, if you have an older than October 24, 2011 MacBook Pro, and didn't install the firmware first, and are working from an erased hard drive. If 10.7 or later never was installed on the drive and that's the case, that may be why it isn't working. Older MacBook Pros require either the original system discs or if they are older than March 29, 2010, 10.6.3 Snow Leopard retail from the Apple web based store.

MiikaH wrote:

When opening my MacBook Pro I get a gray screen and a blinking folder sign with a question mark.

That indicates that the MBP cannot locate the OSX. It can be for three reasons: The HDD is corrupt, the HDD has failed or the connection to the HDD is faulty. If you can, take out the HDD from the MBP, install it in an enclosure, and connect it to the MBP via USB. Start the MBP with the OPTION key down. If the HDD is displayed, click on the HDD and if it boots the MBP, then the internal SATA connection is faulty. If it will not boot the MBP, then the problem lies with the HDD.

I attempted to Reinstall Mac OS X Lion through Internet Recovery, by holding cmd+R at start-up. Then I got a window where I am asked to select the disk to use, but the screen where the disks are supposed to appear is empty.

I also tried the Disk Utility, but the Verify Disk and Recover Disk options are grayed out and cannot be selected.

These signs suggest that the HDD has failed and a replacement will be necessary.

Ciao.