The Legend of Narcissus

As legend goes, Narcissus was a young man who knelt daily beside a lake to contemplate his own beauty. He was so fascinated by himself that one morning, he fell into the lake and drowned. At the spot where he fell, a flower was born, which was called the narcissus.

The following version of the aforementioned legend, I read in a book, which referred it to another book.

When Narcissus died, the goddesses of the forest appeared and found the lake, which had been fresh water, transformed into a lake of salty tears.

"Why do you weep?" the goddesses asked.

"I weep for Narcissus," the lake replied.

"Ah, it is no surprise that you weep for Narcissus," they said, "for though we always pursued him in the forest, you alone could contemplate his beauty close at hand."

"But ... was Narcissus beautiful?" the lake asked.

"Who better than you to know that?" the goddesses said in wonder. "After all, it was by your banks that he knelt each day to contemplate himself!"

The lake was silent for sometime. Finally it said:
"I weep for Narcissus, but I never noticed that Narcissus was beautiful. I weep because, each time he knelt beside my banks, I could see, in the depths of his eyes, my own beauty reflected."

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Now two questions haunt me

Q1. Did Narcissus go to the lake to admire his own beauty or the beauty of the lake which was reflected back to the lake in the eyes of Narcissus?

OR

Q2. Were Narcissus and the lake too involved in contemplating oneself that they were unable to notice each other's beauty?

PS: Do give your opinions.