So lets clarify:
The living room was a two way function (two switches operating the same light)?
and the kitchen light is on a one way single gang switch and only works when the living room light is on?
So kitchen light and living room light are not on the same switch plate (double gang switch)?
If that is true the connection that is incorrect sounds like it will be at the living room light fitting, providing no junction boxes in the ceiling void.
The loop between living room light and kitchen light has been cross connected and only when the the living room light is on, is live being supplied to the kitchen part of the circuit.
So your living room light fitting (ceiling rose) will have an incoming live, neutral and earth then an outgoing live, neutral and earth which feeds the kitchen light. This is the loop and all the lives should be connected together forming a live loop (but not at the live side of the fitting) separate of everything else, if a ceiling rose this will be the central terminals on the rose, if not then a connection block and the neutrals should be terminated at the neutral side of the fitting.
Then a live feed to living room switch and a switch live that returns to the live side of the fitting. The live feed to the switch should be terminated in the live loop (so three cables in there) and all earths together in earth terminal.
I would expect the live loop and switch cables to be red and neutrals to be black.
Now what you need to do is identify the loop in lives and the switch cables.
As it seems they have been mixed up, as I suspect the outgoing live to the kitchen is terminated at the live side of the living room light and not in the live loop. Therefore when the switch for living room light is on, the kitchen light will function but when off will not.