How to get this iPhone off of lost mode?

My dad bought an iPhone 5 from someone but it's in lost mode and I don't know the pass code and neither does my dad. I tried to restore it on iTunes but it said It wouldn't work because it was on lost mode. Can someone tell me how to restore it and take lost mode off?

Have you tried taking it to a cell phone store to see if they could fix the problem.

You don't. The person who lost the iPhone locked it. The person who locked it can unlock it with the correct password. Chances are high that your Dad bought a stolen phone (not knowingly). Find the person who sold the phone to your dad and get the money back in exchange for the useless phone. Assuming that is not possible, turn the phone in to the nearest police department and be prepared to provide a description of the person who sold the phone and other details.

If you can't find your device, use Lost Mode right away to lock it with a passcode, display a custom message on the screen, and keep track of its location. Lost Mode is available with iOS 6 or later.

You can lock an iOS 5 device or a Mac, but you can't track it.

Important: If you lock a Mac, you may not be able to locate it, and you won't be able to erase it remotely.
Use Lost Mode or lock a device
Sign in to icloud.com/#find with your Apple ID (the one you use with iCloud).

If you're using another iCloud app, click the app's name at the top of the iCloud.com window, then click Find My iPhone.

Click All Devices, then select the device you want to track or lock.

Click Lost Mode (iOS 6 or later), or Lock (iOS 5 or OS X v10.7.5 or later).

Lost Mode button in the device's Info window
Follow the onscreen instructions, keeping the following in mind:

If your iOS device already has a passcode, that passcode is used to lock the device.

If you're asked to enter a passcode, that passcode will be required to unlock the device.

If you're asked to enter a phone number, enter a number where you can be reached. The number appears on the device's locked screen.

If you're asked to enter a message, you may want to indicate that the device is lost or how to contact you. The message appears on the device's locked screen.

Note: If you forget the passcode, or if you set an EFI firmware password on your Mac before it was lost, then lock it and later find it, you may need to take it to an authorized repair center to unlock it.
If your device is online, it locks and tracking begins (if applicable). If Location Services is turned off on the device, it's temporarily turned on to track your device's location. A confirmation email is sent to your Apple ID email address.

If your device is offline, the passcode lock and tracking (if applicable) take effect the next time it's online.

If you used Lost Mode, you see the device's current location, as well as any changes in its location on the map.

Lost Mode tracking on Find My iPhone map
Stop Lost Mode or change your contact info
Sign in to icloud.com/#find with your Apple ID (the one you use with iCloud).

If you're using another iCloud app, click the app's name at the top of the iCloud.com window, then click Find My iPhone.

Click All Devices, then select the device that's in Lost Mode.

Click Lost Mode, then change the information or click Stop Lost Mode.

Of course an iPhone is placed in lost mode for a reason. Even so there likely would be iCloud activation lock to deal with & nothing you do would get past that.