Can I transfer or print my text messages on my Lg Envy touchscreen phone

You can email them, then print.
I held my finger on the message for a few seconds and it asked what I want to do - I selected forward and emailed them to myself.
One at a time...

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

Actuall, a special designed android data backup app could help, just few simple steps to transfer everything from your phone to computer, and you don't need to root your phone, just need enable usb debugging on your phone.
Android Manager for Windows Mac OS

"Email My Texts SMS" App is a very simple solution.
It allows you to email them, save the email or print the email. It is easy to use.

BitPim will retrieve your SMS or text messages. You can view and/or browse thru them, and there is also an export and print option.

The only alternative to do somethign like this would be to forward the text message to your e-mail and then print it from your computer. If you can not retrieve the messages and they are saved to your phone,you may need to obtain a subpoena and submit it to your carrier.

To transfer data from your phone to computer, you can try some data backup softwares, and I think it can be easier with an android assistant tool,
you can save a lot of time to transfer or backup text messages, contacts, photos, and other media files like videos, music files.
Transfer Text Messages from Android to Computer PC

install the LG CU500 pc suite software on your PC, attach the data cable from cell phone to pc and transfer data to your pc.

no u cant or u should write the sms text messages and open a new microsoft word document and type it their is no way to copy ok please rate me