My Fiance and I have made the LAN server work before, but with my new laptop it seems to not work. We keep getting Java errors and it doesn't show that my world is open to LAN. On the other hand, it shows it when he opens his LAN yet I get the same Java errors.
1) Make sure your Java is up to date. You can go to http://www.oracle.com/ for more info.
2) Make sure WindowsDefender, and/or your antivirus, isn't blocking Java. Either disable it, or make an exception.