The Lutheran approach to election is that such passages on the topic are written for our assurance, that in Christ, salvation lies entirely outside of our powers (hence alien/imputed righteousness) and in the hand of God. We didn't choose Christ, but Christ chose us.
We hold to while the elect are those who will in the end be saved, it does not mean we can speculate and go beyond what is hidden to us in regards to God's inscrutable will. What does that mean? The rational approach would be to assume since salvation is all of God and election is of some, it must mean God doesn't desire to save all.
Luther rejected that. He warned against such thinking in his Bondage of the Will, his sermons, his Commentary on Genesis, etc. To him the hidden God must be distinguished from the revealed God. The revealed God is the Incarnate God who took on flesh via the virgin birth, obeyed the law on our behalf, and paid the penalty for our sins on the Cross. That revealed God is our Gospel who comes to us in Word and Sacrament. And He desires to save all yet not all are saved.
Why are some saved and some aren't if God wants to save all and salvation is entirely all of God, not of anything in our fallen enslaved wills? That is where Luther said we are to shut our mouth since it is forbidden for us to inquire into. To him, the hidden God is the God of law who hides Himself from us sinners, since no one can see Him and live.
So in that very sense, his distinction between the hidden God and the revealed God is tied to his distinction between law and gospel.
To him, the gospel is Christ crucified for us. And that is the Word of salvation that Christ comes to all with in the mean of grace. And the fault rests with those who does not receive Him. In other words, while salvation is all of God, damnation is entirely on us. God's will to save is indeed earnest.
Luther refused to get into the thinking if God doesn't save all, He must be a weak God. It is enough for us to know that He who elects us is able to both convert and keep us.
And for Luther, holding to salvation is all of God while affirming He wants all to be saved are actually twin ways he saw as assurance to us.
In his view, even if God's word that Christ died for us is rejected when God works grace on us via Word and Sacrament , it still stands. It isn't contingent on our faith or not for it to be true. Why is it assurance to him?
In his view, what's true for all (God's atonement and saving will/grace) becomes objectively true for us personally. In other words, in his view, we can only know Christ died for us personally only if He died for all. Likewise, we can only know He desires to save us with His grace if He truly wants to do so for all.
Luther rejected any idea we can have assurance God wants to save us or Christ died for us if we look to own faith. To him, that would be faith in own faith. In his view, faith alone looks outside ourselves. Look outside to what? To the salvation that lies outside as given unto us in Word and Sacrament.
To him, salvation being all of God tells us we can't look inwards to be assured given if we are honest with ourselves, we can only see the very sinners that needed to be redeemed in the first place which isn't assuring. Likewise, God's earnest desire to save and His providing atonement for all means we don't have to look at own faith or anything insides ourselves to see if He died for us or wants to save. It is objectively true based on fact it is for all. And what is objectively true means we can look outside ourselves, not inwards. Hence, faith alone clings to what God gives and offers in Word and Sacrament, that is Christ's work being delivered.
And that brings me to my next point: Lutheran election is both Christological and sacramental. In Luther's view, our predestination shines when we can say, "I am baptized. I am God's dear child because of that." Or when the words of absolution are spoken to assure forgiveness that Christ won at the Cross is still with us. Or when He delivers His Body and Blood in the Eucharist. He is truly present in Word and Sacrament to deliver Himself and His forgiveness for our outwards, objective assurance. And we rest assured in Christ given unto from outside ourselves in Word and Sacrament, we have assurance we are of the elect- in Christ.
Finally, Luther's doctrine of a true believer can fall away in the end and be lost, but God will preserve His elect is an extension of his doctrines of hidden God/revealed God distinction, law and gospel distinction, and understanding of the objective Word being true and remaining true for all even if rejected.
He affirmed that if a person falls away in the end, it isn't because God doesn't desire to save such a person if we go by revealed will. Why some remain in the faith and some aren't is again none of our business.
The passages exist on assurance and apostasy as law and gospel passages. Apostasy warning passages are really law passages to warn a believer who has fallen into sin and is comfortable in that sin to afflict him with need for contrition and desire for forgiveness. Assurance passages (including election ones) are really gospel passages to assure and comfort those who feel weigh of their sin and desire the forgiveness the gospel offers.
This law and gospel message also applies to how to preach to the lost as well. And the two go hand in hand in that instance. The lost needs law to know need for forgiveness and needs to hear gospel that shows God's love to have forgiveness provided and available to them if they repent and receive by grace through faith alone.
That was Luther's view of what God's word of salvation say. And such Word in his view makes the sacrament. And it remains true even if one takes it in bad or no faith (as in Judas).
Luther, while predestinarian in view, would have us look to God's objective word given to us from outside ourselves in the means of grace. And we find comfort in Christ crucified for our sins with us, we found and locate our predestination. What he opposed doing is make predestination the central focus and in fact forbid debating over the subject. He feared speculations into it leading to either freewill synergism or limited atonement can undercut assurance (and indeed railed against both).
That's Luther's and Lutheran election doctrine in a nutshell.
Here we stand.