All I know is that you need a computer and Android SDK. That is the legal way and doesn't void your phone's warranty.
The LG Vortex runs on Android and as of now, no applications supported by Verizon are available that allow for on-device screenshots.
Both posts above are correct:
There are NO apps that can take a screenshot without root access, which granting them root access voids your warranty and nobody here can help you with anyway.
However, you can take screenshots without messing up your phone using the Android Software Developer's Kit and a USB cable to connect the phone to the computer. I don't know how offhand, and a quick look at developer.android.com doesn't pull much up with the work filters in place on the computer I'm on V_V... But yeah, you can do it this way without impacting your warranty, just have to find out how from someone who knows I guess.
There's a tool in the sdk called the Dalvik Debug Monitor (ddms) that allows this. If your device is connected it's as easy as launching the tool and going Device -> Screen capture. Then it allows you to save the screen capture to a file.
If you're really interested in the details, you can download the sdk at http://developer.android.com/.