The contacts are stored in internal memory, not on the SD card.
If you had your contacts set to sync with your Google account on your old phone (log in to your account via a browser to see if they're there), then you just need to sync your new phone.
Alternatively, the standard Android contacts app has an Import/Export option under settings - I assume your LG will have one, too. In which case, simply export the contacts from your old phone to the SD card, then pop the SD card in the new phone and import.