Is it permissible to lie in order to obtain a leave of absence for i'tikaf during the last ten days of Ramadan?

If the leave is rightfully yours and does not harm the work, then there is no objection to the method mentioned for obtaining it, if no other method is possible, provided that your intention is tawriyah (allusory speech) and not outright lying. Tawriyah is permissible when there is a need for it. Ibn al-Qayyim reported the permissibility of lying to oneself and others if it does not involve harm to others and is a means to attain a right. Ibn al-Jawzi holds that lying is not forbidden for its own sake but for its harm, and it is permissible if it is a means to achieve a permissible objective that cannot be attained except through it, and it becomes obligatory if the objective is obligatory, while preferring tawriyah. Al-Nawawi affirms that lying is permissible or obligatory to achieve an objective that cannot be attained except through it, if the objective is permissible or obligatory.