Hey B! I'm Blake from Home Depot's online community. The water filter that you are inquiring about (LT600P / 5231JA2006A) is the correct water filter for your LFX25975SW. This is an LG factory replacement part.
Anytime you replace a water filter I recommend my customers run a gallon or so of water through the water dispenser and throw away the first batch of ice made to avoid ingesting any loose filter material from the new filter.
I hope this helps B!
-BlakeTheDiyGuy on our How-To Community: http://community.homedepot.com/