بسم الله الرحمن الرحيم
When he took an oath that he won’t tell a lie then he must have fulfilled it. However, after telling lie first time, he will be required to pay kaffarah and the oath came to an end.
و تنحل اليمين إذا وجد الشرط مره (الدر مع الرد 5/605، زكريا)
However, it is necessary to avoid telling a lie in any case.
Allah knows Best!
Darul Uloom Deoband