You say it doesn’t work - do you mean binding the lights to a group doesn’t work, or the bind works, but the dimmer switch doesn’t control all the lights?
I managed to bind a button to an (ikea) blind. I had to repeat the process several times, but it eventually worked. I detailed the whole process here. If it’s a binding problem this might help?
Regarding the LevelControl, I looked at my Zigbee Button (that controls the blind) and mine is “Type: out”, not “in” like yours, so that could be a problem as you suspect? I can’t find any documentation that explains what the “Type” means, but I agree it makes no sense for a button to only accept commands coming “in”!