Unfortunately, not directly from phone to phone. However, there are a few ways to move them.
First, if you have an SD card on your phone, and the new phone will actually read the card, you could transfer all the music from your phone to the card, and then place it in the new phone. Leaving the music either on the card or transferring it to the phone.
Second, if the new phone will read the new card, but will not allow for service using that card, you could follow the above, skipping the 'leave music on card' part. Transfer the music to the phone and then reinsert the card for the LG.
Third option, which would actually probably take less time and effort, would be to use a USB to transfer the music from the phone to a computer and then from the computer to the LG.
Fourth option, which would take the longest, email all the files to yourself from one phone to the other. This option assumes that you have service still on both phones.
Personally, I would suggest option 3, as it takes the least time, and you can also leave a back up copy of all the music on the computer.