On-line research returns the following information-
The instructions for this are in your phone manual. If you have no manual go to the LG Website at
www.lg.com under support.
After your software connects, you should then be able to backup your text messages, among other functions available for your phone.
If this does not work, you can try to get a free account at
myphone.microsoft.com, and sync your text messages online that way. They then can be accessed online, saved to computer individually, or as a zip file from there. However, Microsoft will be ending the Myphone service at the end of this month, so you will have to have this setup prior to that. At which time it will back up your online setting to a skydrive account for you.