Luther didn't teach single predestination but double predestination in his book The Bondage of the Will. For instance in denying the existence of human free will and ascribing everything that happens to God he said:
“I will here bring this little book to an end, though I am prepared if need be to carry the debate farther. However, I think quite enough has been done here to satisfy the godly and anyone who is willing to admit the truth without being obstinate. For if we believe it to be true that God foreknows and predestines all things, that he can neither be mistaken in his foreknowledge nor hindered in his predestination, and that nothing takes place but as he wills it (as reason itself is forced to admit), then on the testimony of reason itself there can't be any free choice in man or angel or any creature.” page 293, The Bondage of the Will, Luther's Works, Vol 33.
"But if God is robbed of the power and wisdom to elect, what will he be but the false idol, chance, at whose nod everything happens at random? And in the end it will come to this, that men are saved and damned without God’s knowledge, since he has not determined by his certain election who are to be saved and who damned,...” page 171, ibid.
The Formula of Concord, which was drawn up after Luther's death and which Lutherans signed up to, didn't follow Luther on this. It argued that God only predestined people to heaven and not to hell, and that He didn't will that any should be damned.
Luther accepted that God according to His revealed will in Scripture willed to save everyone through Christ, but also taught that God has a hidden will of Majesty whereby everything that occurs can't happen without God willing it to happen since He is almighty, and if anything could happen against or outside of His will He wouldn't be omnipotent. Commenting on Christ's lament over Jerusalem (Matthew 23:37) he wrote:
“It is likewise the part of this incarnate God to weep, wail and groan over the perdition of the
ungodly, when the will of the Divine Majesty purposely abandons and reprobates some to perish..." page 146, ibid.
Luther argued that God's foreknowledge of all future events was based on the fact that He had willed the future to happen as it does and this was why He knew for certain what would happen. So since God didn't just foreknow who would be damned, but willed them to be damned, it followed He predestined them to be dammed. Lutherans who follow the Formula however argue that whilst God foreknows the future He doesn't determine who will be damned but only determines who will be saved and predestines only them. This of course leads them into the contradictory position of saying that one cannot say that God doesn't will to save the damned even though He doesn't predestine them to be saved. However Luther disagreed. If God only predestines some to be saved, it follows the reason He doesn't predestine everyone to be saved, is because He doesn't will to save everyone - this was Luther's position in The Bondage of the Will.
Lutherans take their position of single predestination from Bible verses which say God wills to save everyone, such as 1 Timothy 2:4, and use them as determinative in any understanding of God. Luther on the other hand understood such verses only within the context of God desiring through Christ to save everyone. However at the same time he held that, according to God's omnipotent will, everything that happens is governed and willed by Him to happen as it does. Luther interpreted Romans 9 as teaching predestination to both heaven and hell. Lutherans on the other hand try and interpret Paul in Romans 9 as teaching that God only predestines people to heaven.