I'm not sure .. I've never had experience using LW on a network. If the two computers are networked, then he 'might' be able to see the files anyway. lol But that depends on permissions set in both the networking on each computer & folder access permissions.

Do you two have iTunes on your computers? iTunes can share libraries across a network if the option is turned on. And if the option is also enabled on LW, then he could see your iTunes LW shared library on his iTunes. Whilst iTunes can share the iTunes-LW playlist as that's all it is, then the songs can be played but not copied.