Board Thread:TV Show Discussion/@comment-5021198-20160627053544/@comment-25402783-20160627072406

Gonzalo84 wrote: We got confirmation that Jon is Lyanna's son, but not that he's Rhaegar's

Who else could it be? We hear Lyanna say: "if Robert finds out, he'll kill him." At that point, Robert wanted all Targ children dead, so it's clear that Jon is Rhaegar's son. That's why Lyanna wanted Ned to keep Jon safe.