Yes ofcourse a female lieutenant officer of Indian Army can give UPSC civil services exam without leaving the job if your preparation is well enough. As it must have been in your knowledge that UPSC CSE is one of the toughest and crucial exams in India because of its vast syllabus, it becomes more harder for aspirants doing job since most of their time is invested in their work. But still, if one gives their extra effort and smart and hard study, everything is possible.

There is no restrictions in appearing for the exam since you must have been of age 21 or above and have a graduation degree if you are an officer in Indian Army.