It is better to phrase what Confessional Lutherans believe by what is contained in their confessional documents. Since God works faith in man referring to Jesus as 'the Author and Perfector' of ones faith and God will 'save who He will' save, it is incumbent upon the Christian to humbly kneel and stay out of that which would be considered God's business.
Luther's statement 'Justification by faith' is a Scriptural echo of the Apostle Paul. As far as having to be chosen to have faith, how does a human quantify the mind of God in this matter? We KNOW from Scripture that election to salvation occurs, it is a fact. As the segment 'Of the Election of Grace' states that the 'Universal Gracious Will of God embraces all men' but the 'Election of Grace' embraces some. The seeming disparity has to wait for the light of heaven to be resolved.
Not all things are knowable, but the things needed for salvation and a God-pleasing life are; they reside in the pages of Scripture.
Your first staement appears that Luther thought faith was a 'work'. If it is a 'work' it is God's work not man's.