Eglė actually means pine in Lithuanian, not spruce. I am learning the language and I know the legend of Eglė Žalčių Karalienė quite well. That story explains how the pine tree, amongst others, came to be, which is why the word Eglė means pine.
Egle is a Greek name, she is one of the three Graces and it means "splendour, brightness". It's feminine and it is used in Italy. You can find it in the form of "Aglaia".