Thanks for the info.
If you have a few moments, can you open AirPort Utility (Hard Drive > Applications > Utilities > AirPort Utility), click Manual Setup, then click the Wireless tab below the icons.
Radio Mode should be set to something like 802.11n (802.11b/g compatible). If you have it set for 5 GHz, the LG could probably "see" the network, but may not connect.
Check the Wireless Security setting as well If it's WPA/WPA2 Personal, (I believe this is the default setting for the AirPort Express) try changing to simply WPA2 Personal. Update to save changes and see if that helps. If you don't see that choice, hold down the option key on your computer when you click on the Security selection box.
If no luck there, I would try temporarily changing the Wireless Security to None to make sure you can connect that way. Then, it may a trial and error process.
WPA/WPA2 is supposed to accept a regular password without having to enter a network "key", but that might be something to check as well. You can find your network "key" by clicking the Base Station menu (at the top of the screen near the Apple icon) and selecting Equivalent Network Password. It's a very long series of letters and numbers.
Please post back on your progress.