Is it permissible to say that Allah inscribes the names of pilgrims each year, and that whoever's name is not inscribed will not perform Hajj, in order to comfort those whose names were not drawn in the Hajj lottery?

There is no harm in saying that Allah Almighty commands the angels on Laylat al-Qadr (the Night of Decree) to record what will happen in that year, based on His saying: "Indeed, We sent it down on a blessed night. Indeed, We were warners. On that night, every wise matter is made distinct" (Ad-Dukhan: 3-4). The scholars have mentioned that on this night, what will happen in the year, concerning life, death, provision, and rain, is decreed and copied from the Mother of the Book, and that a person will only attain what has been written for him. Therefore, all that befalls him, whether a blessing or a calamity, is by the decree of Allah Almighty.