I have two lamps and I need to connect them on 1 tri-pole socket and then plug the socket on the wall socket

the thing is.. I can 3 inputs at the socket (E, L, N) E = earth.
my problem is... the cable for connecting the lights and the socket together only has two smaller cables (blue and brown) inside instead of three only. Shall I connect them without earth? And also is it possible to connect them together or shall I need a separate socket for the second lamp?
thanks

It would be a good idea to let us know that you are not in the US and what country you are in (I assume the UK).
This way you can get the proper help.