Upvote:1
Yes, Lutherans believe in Freewill, but a Lutheran would structure your example a little differently, and have a different interpretation of it. An interpretation consistent with Lutheran theology would be that none of the 100 people can save him or herself, in the words of the Small Catechism
I believe that I cannot by my own reason or strength believe in Jesus Christ my Lord, or come to Him; but the Holy Ghost has called me through the Gospel, enlightened me by his gifts, and sanctified and preserved me in the true faith; [Explanation of the 3rd article of the Apostle's Creed].
The SAR in your example is God the Holy Spirit, and the rescue is effected by Jesus' death and resurrection which saves some number of the hundred people you identify. But Lutherans understand that although Jesus' death and resurrection are available to all 100 people in your example, a few (though we don't know how many, nor do we know who they are) may reject the promised salvation through their exercise of Freewill.