I have vertical lines on an 37LG30 appear after 15 minutes on

The so called PLASTIC STRIPS un correctly called by xxxx1000 is called FLEXIBLE PCB, they are brown in color and easily damaged, they are connection to the LCD panel by Ultrasonic welding NOT SOLDERING and this some time can be the cause of the problem. If any one ever take the LCD PANEL part they will know what they are talking about.
The problem you have can be the the T-CON board, maun board, worst case will be the LCD panel itself.
But first thing to inspect will be the power supply DC filter caps. Next is to reseat the ribbon cable from the LCD panel to the T-CON board (this board is mounted under the metal shield).
So inspect the inside and post back what you find.
If you are going to DIY and have proper tools, electronics knowledge, and know safety precaution then please read on:

Please see my basic troubleshooting guide here:
http://www.fixya.com/support/r5093881-lcd_flat_panel_tv_troubleshooting_guide
http://www.fixya.com/support/r6150077-basic_lcd_monitors_troubleshooting
Failed TV and Monitors: http://s807.photobucket.com/albums/yy352/budm/
Learn about bad caps: http://en.wikipedia.org/wiki/Capacitor_plague
Parts: www.shopjimmy.com
Capacitors kit: http://lcdalternatives.auctivacommerce.com/Default.aspx he can make you a set of caps.
Or www.digikey.com just make sure to use caps with low ESR, 105c, high ripple current, long life rating such as PANASONIC FM or FC series.