Having reread a the new Pottermore moments and chapters I cannot see anywhere JK mentions Remus' father having passed away, and more specifically he refused to return to live with Lyall so as to not endanger him. With that in mind, why did Lupin not let Teddy grow up with his grandfather Lyall, rather than let Harry, who was still 17 or so?
There's no specific confirmation provided in any of the Potter novels as to whether Lyall Lupin is alive or dead after the end of Deathly Hallows, nor has there been anything released in any of the additional materials to confirm why he was (or wasn't) considered as a guardian for Teddy Lupin.
The latest biography provided on Pottermore sheds very little light on his current whereabouts, nor does the Potter Wikia have any further details to offer on him. Short of asking JKR directly, we may simply never know.
As to the specifics of your question, Teddy didn't grow up in Harry's care. He was, in fact raised by his maternal grandmother; Andromeda Tonks although he did regularly visit the home of his godfather Harry Potter ("at least four times a week") as he was growing up.