"of the prophet was heard in reply, “Oh king, live for ever. My God hath sent his angel, and hath shut the lions’ mouths, that they have not hurt me: forasmuch as before him innocency was found in me; and also before thee, Oh king, have I done no hurt. SL 45.1"
"Then said Daniel unto the king, O king, live for ever. My God hath sent his angel, and hath shut the lions’ mouths, that they have not hurt me: forasmuch as before him innocency was found in me; and also before thee, O king, have I done no hurt."
EGW directly quotes Daniel 6:21-22.
"“Then was the king exceeding glad for him, and commanded that they should take Daniel up out of the den. So Daniel was taken up out of the den, and no manner of hurt was found upon him, because he believed in his God” ( verses 22, 23 ). Thus was the servant of God delivered. And the snare which his enemies had laid for his destruction proved to be their own ruin. At the command of the king they were cast into the den, and instantly devoured by the wild beasts. SL 45.2"
"Who through faith subdued kingdoms, wrought righteousness, obtained promises, stopped the mouths of lions,"
Both passages refer to Daniel being saved from lions through faith. Hebrews 11:33 is a general statement, while EGW's passage is a specific retelling of the Daniel story, making it a thematic parallel.