Confusion about *G lounge access is one of the great FT traditions. The
Star Alliance website is fairly clear:
While the phrasing "in conjunction with..." is slightly ambiguous, note that every
other entry on that page -- e.g., "International Business Class" -- specifically states "Customer must be departing from the local airport in International Business Class" or the equivalent. Since the *G entry does
not state that the customer must be departing internationally
from the local airport, I think the intent is clear.
However, some of the US clubs (especially the Envoy Lounge in PHL) are notorious for ignoring this policy -- see
this thread. There are other threads about similar issues, but the consensus is clear that *G gets you access to every lounge with the *G sign outside if you have a same-day international flight downstream (you do
not get access at your terminating airport). This is respected by most *A airlines. Unfortunately, US famously ignores the rules, and SQ famously makes up their own rules.
And, for what it's worth,
United's policy specifically allows international F/C customers lounge access at every domestic connection
if they are departing that airport in a premium cabin.