Can You Print Out Text Messages on the LG Optimus G ?

If you need to print the text messages from your phone, you should backup or transfer them out of your phone, and save as printable format on your computer,
How to Print out Text Messages from Android Mobile Phones

and it can also be available for contacts.

Android Backup Assistant Backup Android Phone to PC

you can use this backup assistant to transfer more data out of your phone.

If you're looking to print out android messages, How to Print Text Messages software is the best choice which lets you do it in just a few easy steps. It offers a convenient solution for all Android users to print out messages.

How to Print Out Off Text Messages from LG Optimus etc

Vibosoft LG SMS print app must easily pull you out of despair when you deem it's necessary to print out SMS from LG :
http://www.vibosoft.com/mobile-phone/how-to-print-out-text-messages-from-lg.html

You can also try iPubsoft Android Desktop Manager. Free Trial: How to print text message from LG to computer. you can copy messages from LG to pc quickly, this is a comprehensive software, you can also transfer and save contacts, photos, songs, movies from android phone to computer. High compatibility, it can support 200+ android phone. such as Samsung, HTC, Motorola, LG, Sony, etc. How to Print LG Phone Text Messages Conversations Out