LGSIL stands for Low Grade Squamous Intraepithelial lesion. Its a medical term given to a level of cervical dysplasia (basically abnormal cells) and is detected through a Pap smear. An LGSIL result means that mild dysplasia, more than likely caused by the human papillomavirus (HPV) has been detected. It is the most common classification of cervical dysplasia, and in most cases, clears up on its own within two years.
With regards to navy boot camp, I honestly don't know, my brother is in the Navy so I know how strict they can be with illnesses etc. Just make sure you let them know in good time, and make an appointment with your doctor to discuss it. If necessary, you can ask your doctor to write you a medical note.