Hello again and thank you for the replies.
I already know that the Theatre does not support matrices and I suppose the best solution for me would be a splitter. I have already tried to use my current Atlona switch (AT-UHD-SW-52) but I get no communication between the Theatre and the LG (although I get communication between the Theatre and the projector (epson)). Furthermore I get no picture at all from the LG (although I get picture on the projector). I get no audio from the LG. I played around with the EDID settings, the autoswitch, etc but no luck. I have tried different cables but still the problems persist. It seems that the LG will work only if it is directly connected to the Theatre.
I run all my sources (apple tv and nvidia shield pro) through the theatre so all I need is a splitter that has two mirrored outputs, cec passthrough, earc, 4k, and hdr.
Last but by no means least I tried a ugreen switch which has all the above except mirrored outputs (you need to press a button to switch from one output to the other) but again no luck…
Any ideas?????