Is it permissible to lie to one's husband by claiming that there was no exchange of photos or closeness in a previous relationship, knowing that the husband requested honesty in the answer and swore an oath to that effect, and that dishonesty could lead to divorce?

The husband's question about a previous relationship in this manner is impermissible, and you are not obliged to answer it. You were right not to inform him about the sins you committed, for your lying to him in this situation is permissible to conceal a sin. You may swear an oath using al-ma'arid (ambiguous statements) and al-tawriyah (double entendre). Furthermore, the intention to marry does not justify a forbidden relationship. Therefore, repent to Allah with sincere repentance from all sins and transgressions.