Yes, it is Sanskrit: the word lIlA of doubtful origin (the root lI means to cling) means sport, and the suffix vat means one who has (in ths context), together it means graceful or charming. the last -I is feminine suffix, and lIlAvatI means a beautiful woman.
The I means the long ee sound of English, A is the long a sound in car, the t is soft as in French pronounciation, the l is clear as in English, the a is indeterminate schwa, and the v is a voiced unaspirated labiodental, closest to the English sound at the beginning of water. In some modern Indian languages, the va can become bo, and the distinction between soft and long may disappear. Stress is not a marked feature in most of these languages.