It is very plain that the statement that certain names would NOT be blotted out of the Book of Life implies that names may be blotted out. God does not hold out empty threats (Rev. 22:19).
An illustration might help here. We know that churches keep a careful register of their members. We know that generally speaking these members may be true Christians, but in many cases alas! are mere professors. Suppose the Lord examined these lists with a view to retaining the names of believers, and blotting out the names of mere professors. We know what would be the result.
In 2 Tim. 2:19, we are told, so great will be the deadness and coldness of the Christian profession in the last days, that it will be difficult to know, who are Christians, and who are not. The test given to the Christian is that all those, who profess the Lord's name, should be marked by departing from iniquity. (2 Tim. 2:19). But with the Lord, who can read every heart, no mistakes are made. His eyes pierce the thin veneer of a false profession. His eyes infallibly recognize those who trust in Him. In this Scripture it is a question between the real and the false, between real believers and empty professors. It assures us that the names of true believers will never be blotted out of the Book of Life, for we read, "Nevertheless the foundation of God standeth sure, having this seal, the Lord knoweth them that are His." (2 Tim. 2:19).