I presume that you are not flying in either F or J and that your *G status is not through either LH or LX. Thus, your access is as a *G from another *A carrier and solely through your *G status and no other reason. I also presume that as your daughter is flying independently on another carrier that she is not a very young child.
If so, here is the *A rule. It is clearly displayed on the *A website and it might be helpful if you went to the website and printed out the rules lest you be asked. You will be permitted one guest. That will be either your wife or your daughter.
As a Star Alliance Gold customer, you have access to any member airline lounge that displays the Star Alliance Gold logo. You will need to present your boarding pass for a Star Alliance flight departing from the local airport. If your boarding pass does not carry the Star Alliance Gold indicator, you will need also to show your valid Star Alliance Gold card. You are entitled to a maximum of one guest.
It is possible that a lounge receptionist might except a young child traveling with you, but another adult on a separate ticket is unlikely and with LH will almost certainly draw the standard, "that will not be possible."