I think Ella would be okay with Emily (although both start with the same initial, the ending sounds and number of syllables make them fairly distinguishable) .
While Ella is a name in it's own right, it could be a nn for other El - names including Elizabeth or ones that end in -ella like Gabriella, Arabella etc.
Although I have heard Lily as a nn for Elizabeth, Lily is too much with Emily imo.