Is touching and kissing a close female relative—when the questioner was a teenager—considered zina (unlawful sexual intercourse), and is it permissible for him to lie and swear to conceal this act?

Mere enjoyment of touch, kissing, and the like is not actual zina (fornication/adultery) that entails the rulings of zina. Rather, it is a sin, and the Prophet, peace and blessings be upon him, figuratively called it zina. One must repent to Allah Almighty by abandoning the sin, regretting it, and resolving not to return to it, while concealing oneself and the girl by not informing anyone about this sin. If you are asked about this sin, do not confess to it; it is permissible for you to lie to conceal yourself. If you need to swear an oath, use tawriya (equivocation). A sound repentance is accepted, Allah willing, so do not preoccupy yourself with what has passed. Rejoice in the acceptance of repentance and Allah's forgiveness.