Hmm, it's somewhat odd that someone would use both spellings then (and pronunciations too). This is a small American school though.
Two complicating factors here:
First, the Korean consonent rieul is positioned about half way between how an english speaker pronounces L and R - We actually have an exceedingly hard time pronouncing it correctly, because our natural instinct is to shade it in one direction or the other. Now, probably because we commonly shade the riuel in "il" towards the L, this smears over our pronunciation of the rieul in lo/ro towards the L (일 로
, a factor which is not present in the Ee Lo (이 로
pronunciation.
Further, In a small school, depending on where and how the initial teachers of the school learned the form, they may not have parsed the name of the form; some hyung have names that don't translate directly meaningfully into english (ex: Kong Song Koon), and in I suspect that the thought behind the name doesn't always get passed down along American lines. Sadly, not everyone is curious enough to look - Do they even know that it's the same word (Path/Road)?
South Korean government standardized the romanization of rieul to L in 2000, but that's late in the game and gets ignored a lot.
Also, read the numbers. Some schools may teach Chil Sung Ee Lo before Chil Sung Il Lo, but they are named "Seven Star(Big Dipper) First Path", "Seven Star Second Path", "Seven Star Third Path", etc, etc.
