Since the new king and Ned himself really wanted her back, it's hard to imagine they were, but I'm not sure if this is mentioned anywhere

Ned and Robert weren't friends anymore after the Sack of King's Landing. They only rekindled after Lyanna's death, but before that they weren't on the "same team". It was up to Ned to find Lyanna, not Robert.

How did Ned know to find her at the Tower of Joy? or was this just a stroke of luck

Many will tell you that Ashara Dayne told him, but it is insane to think Ashara would give the location of her brother to a rebel who just helped overthrow the Targaryens. Whatever happened between Ned and Ashara, had nothing to do with the Tower of Joy.

On TWOIAF, it was known that Rhaegar came back from the south(Dorne) to fight in the war. So while Lyanna's exact location wasn't known, they did knew which region she was.

Did Ned know there would be three Kings Guard protecting her?

No, but when he did saw them there, he wasn't surprised. He started to realize what was going on. His conversation with them is mainly an interrogation where Ned wanted them to say what they were there for, even though Ned kind of knew now why they were there.

Did no one question why the Kingsguard were there protecting Lyanna?

Who do you want to question this? Lyanna was the daughter of a Lord who lived far in the North with his head buried in the snow. She only became famous because of Rhaegar, and then because her betrothed became King. But overall, she wasn't nearly as important as them, the others don't really care what happened to her.