Is it permissible for a man to lie and claim divorce in order to marry another woman, while retaining his first wife, and due to the prevalence of temptations in Western countries?

The basic principle is that lying is forbidden and is not permissible except in cases where it serves a greater good or prevents a greater harm, such as lying to one's wife, reconciling disputing parties, or in war. Therefore, it is not permissible to falsely inform a woman that you are unmarried so that she will accept you as a husband, as this involves deception and delusion. It is advised to be truthful in building married life.