LuckyWire is one of many dozens of LimeWire clones (usally based off LW 4 but LuckyWire is based off LW 5.) So yes it is a part of the Gnutella network. I still see people using it from time to time.
Are you having connection problems or download problems?

You need to be connected to the gnutella network before you can search for files.

If it is connection problems, try dropping a gnutella.net file into the LuckyWire preferences folder. http://www.gnutellaforums.com/connec...t-connect.html and it might just get lucky. I presume the LuckyWire preferences folder IS called LuckyWire, so you only need to make that much of an adjustment to the guideline suggestions given in the link about replacing the gnutella.net file.