Star Gold gives access to Senator lounges where available, with one guest. Outside of the LH group, then it is business class lounge, keeping in mind that LX and LH are the only two alliance’s airlines offering first in Europe.
Access to First Lounges is restricted to First passengers as well as HON Circles members. And, yes, First lounges are rather good within the LH group while the difference between business and Senator is limited.
Star Silver gives access to business lounges with no guest at some airports (ZRH, FRA, …).
BA Gold gives access to First lounges excepted Concorde’s. Sometimes though not all the amenities are offered (pre-flight dinner at ORD for instance is different for First passengers with a dedicated room and better wines). In general within the alliance, First lounges are much better than business class lounges or any Senator one.