Adding LED Recessed - 3 Way Switch - Dim Lights
This can't work without smart switches

You can't wire 2-way switches with only twin-and-earth, unles you do something totally evil and dangerous.  If it ever worked before, it was wired horribly.  

You are groping around trying to experiment, which you should not do, but at least you are using the wires properly - reserving green/yellow for ground instead of bootlegging a hot or whatever horrible thing the last guy did.  

The runs from lamp to switch need to be replaced with 3-wire + ground (whatever they call that where you are).  Then we can use 2 of them as what we call "travelers" and have the third for hot/common.  

Your alternative if you can't rewire is to use smart switches, but this will require a module in the first lamp.