This is a misinterpretation of the facts.

LOT is handled by KLM at AMS. This was so in 2008 and it remains so today. Star Alliance golds can access the Crown Lounge only when flying with LOT (though I suspect that if your *G was with a programme other than Miles & More you may have difficulty gaining access). You are flying with TAP so all that matters to you is which lounge is contracted by TAP. This is also confirmed by the Star Alliance lounge finder which shows that only LOT customers have access to the KLM Crown Lounge.

When the lounges in question are "contract" or third party lounges, you really do have to be flying on the airline in question - you cannot "lounge hop" as you could when it is an alliance or alliance-member lounge, and you cannot access any of the other lounges that any other Star Alliance partner may have a contract with, even the lounge contracted by the airline in which you hold status (unless it happens to be the very same lounge that the airline you are actually travelling on has contracted, too).



Safe travels!