I’m sure this is also cultural, but that approach is terrible. Your friend can’t automatically guess you’re lying, not for the first few times, anyway. Of course they’ll believe you if you say you’re too tired to go out. Then they inadvertently catch you or you reject them so many times they start to believe you don’t want to go out with them, not the other friend. All the while they became closer with the other person, who actually did hang out with them.

Stop lying. You’re hurting the friendship. If you care about the person, eventually you’ll have to be an adult and explain why you’re not comfortable with the third person.