I received a LS20031 GPS a few weeks ago and have been trying to get it up and running.
I am able to use putty and other serial applications to receive data from the GPS at the default BAUD rate, but I am unable to send a message to the device or at least it seems to not respond to the message. I had the same experience using MINI GPS application 1.4 in the resources on the products page, as well as GPSFox both do not recognize any incoming messages nor does the device seem to respond to any input messages.
To communicate with the device I have setup a TTL to USB converter in order to communcate with the device at the 3.3 V level. The power supply is 3.3 V. I have read the information from the resource file and followed an online tutorial from sparkfun, but still now luck in getting a decent message from the device or sending any messages to it.