The question of whether God would damn a baby because the parents were too lazy or foolish to get the child baptized frames the whole thing wrong due to the word "because".
Note, in my original example, I gave no reasons why the infant had not been baptized. In the case of both our children, there was a matter of a month or more before my pastor (the bishop) could come the nearly 500 miles and officiate at the baptism. The delay was not caused by laziness or foolishness or misplaced belief, but because of practical matters.
If we simply assume that God saves the unbaptized, we're making baptism meaningless. Might He save them? Sure. If you jumped off a pinnacle, He might send the angels to bear you up lest you strike your foot against a stone.
Exactly, salvation for sinners is up to God. The sacraments assure us that God is gracious to us, but they do not rule out the possibility that God can save the unbaptized, the non-Lutheran, or even the non-Christian by his grace, should God decide to do so. (Note that in Isaiah 45, Cyrus, the Persian ruler, who does not believe in God, is chosen by God -- in fact, even called, "a Messiah" in the Hebrew -- to save the Israelites from their Babylonian exile.)
At the same time, as I wrote earlier, I believe that everyone who ends up in heaven, are there because of Jesus.