Most certainly you can, and that too without having to spend a fortune or two and without having to stress your grey cells. All you need to buy is the appropriate controller board kit from ebay. You would have to mention your LCD panel type (manufacturer name and model number and resolution) to the seller, remember this is not the brand name of your laptop. To find out the manufacturer and make of your LCD you would have to strip it down to reveal the skeleton of the LCD, the information should be imprinted on the back of the LCD, the one shown here is (LG Philips LCD LP150U1-A2 with 1600×1200 resolution).
Based on the LCD type this ebay seller  would program the controller board, and choose inverter and LVDS cable for it. I just received the controller board listed on this page  and it didn’t take me long to fire it up. All I need to do was to: connect the inverter power output to LCD panel, connect the LVDS cable to the back of LCD panel after I removed the previous LVDS cable. Please note, the male connector from the LCD connects to the inverter board in only one way to ensure the polarity, make sure you connect it properly and push it all the way in, else the screen wont brighten up. Do drop me a line if you have any question in this regard.
Here are a few images of my DIY homemade monitor built from a laptop LCD panel which has a resolution of 1600×1200. Total investment was $47. In time I intend to spice up the look of this monitor and build a DIY enclosure for it.
Here is an image depicting the connections for the board. Feel free to ask if the image is not clear enough!