No, the screen cannot be locked. It can be exited by tapping the appropriate exit button. Visit facebook.com/nabitablet for assistance.
Here is a post I found that maybe helpful to you.
Does your child exit apps and stop/pause videos by accidentally hitting the nabi’s buttons or touching the screen?
If this happens to your child, the Lock Any App Screen is a useful app to have installed on the nabi jr, nabi 2, and nabi xd. It is a quick and easy way to lock the buttons, touch screen or both for ANY app.*
Common uses include:
1. Restrict toddlers and kids to the games/app that they like, and prevent them from exiting.
2. Allow toddlers and kids to watch videos with the screen and buttons disabled.
3. Read books or have books read aloud with screen and buttons disabled.
Steps for use:
1. Install the app from the Amazon Appstore.** http://www.amazon.com/Zero-Noise-Apps-Lock-Screen/dp/B00844TM4Y
2. Open the app and tap green ‘Get Started’ button.
3. Open the app your child wants to play and a small Lock Any App Screen app icon will be visible on far right of the nabi’s screen. Long press on the small app icon for lock options.
4. To lock, select from the options available: Screen + Buttons, Screen Only or Buttons Only
5. To unlock, touch the four screen corners CLOCKWISE, long press the small Lock Any App Screen icon and tap Unlock to use the touch screen and/or buttons or Exit to disable the Lock Any App Screen.
*Buttons Lock does not work with some apps e.g. Netflix, MX Player. Only the Screen Lock works.
**Everything Nabi blog provides steps on how to add Amazon Appstore to the nabi (works for nabi jr, nabi 2 and nabi xd): http://everythingnabi.blogspot.com/2012/08/installing-configuring-amazon-appstore.html