Yes, both you and your spouse can apply separately for the Diversity Visa (DV) Lottery. The DV Lottery program allows each individual to submit their own application, even if they are married or in a committed relationship. Each application is considered separately, and if either you or your spouse is selected as a winner, the other can also obtain a derivative visa as your spouse.
It is important to note that both applications should be truthful and accurate, providing all the required information and documentation. Duplicate or fraudulent applications can result in disqualification.