I think your referring to the mechanical looking door with the falcon symbol on it, the problem with this door is that it does not appear to open by any means.
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Your boyfriend might know what to do with it

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Actually just prior to checking this I was exploring the Li's cave. Previously I had found no use for this area, but I thought it awkward that the whole area would carry no meaning so I began to explore it again. Now I have Li's song and its very obvious what to do thank you.